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Rainbow Times Releases Key Endorsements
TOPICS:AIDSbostonendorsementshislgbtqlgbtq rightslgbtq youth of colorlynnmassachusettsnonbinarysalemtransgender
Posted By: The Rainbow Times October 22, 2021
The Rainbow Times' endorsements for Salem and Lynn, Mass. are in; Boston Mayoral endorsement to come
By: The Rainbow Times' Editorial Team—
The Rainbow Times' editorial team has proudly released its Salem, Boston, and Lynn endorsements for Mayoral and City Council races. Each endorsement was carefully considered based on the upholding of progressive values and ideals, support of the LGBTQ+ community, a demonstrated understanding of issues impacting marginalized community members, and those who not only embrace diversity but who are supportive of inclusive practices of municipal leadership.
The team believes there are two levels of competencies needed to be effective in local government. First, cultural and intersectional proficiency is needed to understand and work effectively on behalf of all residents. Secondly, critical municipal issues such as housing, the climate crisis, residents' safety concerns, community members' mental and physical health, infrastructure and development, all must take a front seat when leading municipalities forward. Likewise, those elected to leadership positions must be able to navigate the intricacies of establishing innovation within city government while not leaving behind equitable and inclusive practices and ordinances. Every local issue impacts each and every resident differently. However, due to systemic barriers, such obstacles disproportionately and adversely impact disenfranchised communities.
The candidates who have earned our endorsement have directly demonstrated to our editorial team — based on responses, past voting records, and actions — that they have the competency to not only lead broadly but are people who have already engaged themselves in pro-active roles to effect change for those who are at the bottom of the totem pole, for they are also invested in equity and we see that through their former and current actions.
After receiving written responses to LGBTQ+ specific interview questions, including those based on intersectional identity, issues disproportionately affecting the community at the local level, and extensive research conducted by The Rainbow Times' editorial team, we are confident in the endorsements below. We unequivocally believe that these candidates for elected office will represent the interests of the LGBTQ+ community (and communities of color within and outside of it) with vigor and knowledge, with compassion and logic, with fairness and impartiality placed at the forefront of their voting matters in city government. We are proud to stand firmly with the endorsed candidates and we are unwavering in our support of them, and our process conducted during this endorsement period.
As a publication that focuses heavily on civil rights and educating others about the intersectionalities of our vast identities, the litmus test was not easily passed. We are proud to endorse candidates that are best suited to advocate on behalf of the LGBTQ+ community and the subcultures existing around it, whether they're friends, allies, or family members.
Local government must be willing to make inroads on issues and contribute to producing solutions rather than stalwart them. Councillors should be willing and capable to bring tangible proposals to the table to combat the most pressing needs of residents. Simply standing in the way of progress just "for the sake of it" isn't enough, nor does it fulfill a candidate's responsibility with all of its base, which is most likely comprised of people from all walks of life, races, ethnicities, sexual orientations, credo, religion, gender identity and so on.
Like many cities across the nation and certainly within the walls of Congress, we've seen the devastating impact that Americans have suffered at the hands of elected officials that are not only out of touch with what would benefit the majority of residents in their districts — whose callous lack of responsibility or compassion to the plights of others reaps devastating consequences, thereby threatening the fabric of our democracy. There are obstructionists of all kinds and backgrounds, all racial identities, and so forth. Local government is certainly not immune to it, as has been demonstrated in Salem.
After careful examination of voting records in multiple races, our team found that in Salem particularly, there have been four (4) City Councillors who have been obstructionists to producing results, offering viable solutions, articulating common-sense decisions (or bringing their own plans to the table), and who have been more aligned with the self-serving interests of a few, rather than representing all of their constituents with transparency and inclusion. They act in strife, ignoring any sense of accountability or responsibility to constituents. They do all unabashedly with a sense of impunity. They have been unmoved regardless of facts, experts' advice, educational forums, and have not listened to the outcry of the critical needs of residents. That is not leadership at all, but rather using the people's seat as a bully pulpit, similar to what we suffered through under the Trump administration. We must expect more from our elected officials. All residents across the board deserve it.
Some candidates running for office this election cycle have intently and openly discriminated against the LGBTQ+ community, touting religious beliefs for their prejudicial practices, also most notably in Salem. They have weaponized LGBTQ+ status as if LGBTQ+ candidates or those who are allies and support equality for the members of this community are wrong to support equal rights for everyone. Others have openly made up malicious anti-LGBTQ+ rhetoric that involves heterosexual candidates having affairs with former city officials, etc. — a shameful tactic that is often believed by the most naïve amongst us, or those who want to create division within Salem.
Currently, there is a local onslaught to impose personal religious practices into local government, with some Salem At-Large candidates claiming they will "govern according to the will of God," and will vote according to their faith, regardless of whether human rights may be at stake and no matter what local ordinances and laws are already established. They have gone as far as to state that they support "conversion therapy" against gay and transgender students and adults in Salem, which leads to increased suicide rates, societal shunning, and longstanding mental anguish. The fact that Massachusetts was the 16th state banning gay conversion therapy wasn't something that deterred them from making these false statements to some of our editorial team members and they are not alone in promoting this anti-LGBTQ+ agenda openly — and other times covertly — by letting voters know that gay and trans candidates did not belong in local politics. Factually, the information uncovered was alarming to say the very least. The Rainbow Times will follow up on investigative stories it is working on about this specific hate-filled religious right that has shown up in Salem and is being moved around by other candidates who belong to other marginalized groups, which is the most troublesome aspect of what was uncovered.
As we've seen in national politics, there has been a divisive trickle-down effect throughout the country. Some have expressed desire akin to a freeze-frame in time, remembering what they deem as the "good days," or reverting to the 1950s, a period of time that was stifling, abusive and oppressive for all marginalized groups. It is critical, as a society, that our cities and towns continue to make progress — progress that will earn us all a seat at the table. Progress grows local economies. It ensures a brighter future for the youngest of generations and progressive policies place people, all people, at the forefront. The world moves forward and so must we.
Many, both young and old, strive for equality, human rights, climate control and eco-friendly measures, womens' rights, equal pay, reproductive rights, and gun control. We believe those professing those changes are moving in the right direction to correct the errors of the past, change the current systems of oppression that limit other Americans from having a seat, voice, and vote at the table, and who fight to change America for the better. Most old-school politicians and those who support white supremacy disagree. We don't wonder why they do so.
We must work harder to elect candidates who vow to change the status quo, even when many will resist. Resistance to change without a plausible argument is just born either out of fear and ignorance, or bias and prejudice. There is a plethora of reputable information and published research by professionals of each field that offers plenty of information and education about prejudice and the patriarchy, as a system of oppression that continues to hurt every person under it, other than those in power. To sit idly and do nothing is not an option. To keep the status quo and continue to oppress anyone who is not white is not an option. We have seen where that has taken us, with covert racism just about everywhere and overt racism under Trump — and the rise of white supremacy and domestic terrorism. And, bottom line, we can do better. But, we can only do better if we get out the vote. Words and endorsements are nothing if you don't go out there and cast your vote. Let our democracy work fully by becoming an active part of the process so that you, too, can make a difference.
With growth and change come challenges; with progress comes change and compromise. We must have elected officials that understand the unique set of circumstances that surrounds forward movement. We also need elected officials who are equipped to rise to the occasion, who have the conviction of their words and work, who seek to understand and advocate for others, who strive for inclusion, and who comprehend how critical this point in time is — a time that will make or break so many of us when words and practices have been tainted, twisted and weaponized to gain political advantage or promote policies based on self-serving and archaic interest. We need elected officials who keep all residents in mind and who will work to dismantle the onslaught of attacks against the LGBTQ+ community and all marginalized communities while breaking down barriers to the access of services and who put a sizable dent into the systemic oppression that we know glaringly exists in nearly every facet of life.
After a rigorous endorsement process, The Rainbow Times proudly endorses the candidates below.
Salem Mayor
Kim Driscoll for Salem Mayor
The current incumbent, Mayor Kim Driscoll, has kept Salem moving forward for the past 16 years while serving the residents of Salem with strength, resiliency, intellectual fortitude, and inclusion. Under her formidable leadership, Mayor Driscoll has helped lead Salem to become a world-class city with a booming economy, smart development, and an in-depth understanding of issues relating to the LGBTQ+ community and the subcultures existing within it. For ongoing progress, inclusion, and equity within the Salem borders, Mayor Driscoll is the only choice.
We are thrilled to announce our ardent endorsement of Kim Driscoll once again for Salem Mayor. Mayor Driscoll has fervently stood with the LGBTQ+ community, has committed herself to equity within the city of Salem, and has publicly demonstrated leadership from an inclusive, educated, and innovative process. She has handled the COVID-crisis like a champ while putting the health and safety of Salem residents at the forefront and ensuring the city stays on track and operates as normal as possible to allow our local businesses to flourish. That is not an easy task and something that many other Mayors and cities struggled with last year and even now. Her leadership is unmatched and we are proud to throw our full support behind her re-election bid. Salem's future depends on it.
Our climate concerns deserve someone who will support eco-friendly solutions while standing against all types of prejudice. We know Mayor Driscoll has delivered substantial solutions already that have safeguarded people of color, and LGBTQ+ youth. The creation of the Salem Race Equity Task Force (SRETF) is one of those examples of her leadership in the wake of the national exposure that the murders of George Floyd and Breonna Taylor brought to life. With the SRETF, there is a solid foundation and an intentional effort from the Mayor to tackle issues that minority people experience in Salem. That shows that Mayor Driscoll sees BIPOC people and all, and she delivers on her commitment to continuing a Salem that is inclusive of all, and where accountability is present. It's not about perfection, it's about a record of fighting for what's right and protecting those who need it most while protecting the environment, maintaining our history, developing coalitions with community partners to tackle the most pressing needs of Salem residents like housing, affordability, development, and infrastructure. Salem has been in the process of transformation, a transformation that has led us to this point of growth. That can only be accomplished with a formidable leader that delivers on the promises made to us all. Mayor Driscoll is a fighter and doesn't give up, even when there have been obstructionists on the Council to halt any meaningful progress and have tried to deny many Salemites of basic human rights, such as the right to be able to afford housing and support ADUs, so that those who work locally and contribute to the wellbeing of a vibrant city can afford to live here too.
Mayor Driscoll walks the walk and talks the talk. She has been out on the campaign trail not merely to get a vote but to get to know the concerns of the residents and to listen to how she can continue to improve the city as a whole. She invests herself deeply in city issues and that includes going into the trenches with others and digging deep to get the job done. No one person will agree on every single decision a Mayor makes — that is an impossible task. What we know is that Mayor Kim Driscoll is a powerhouse that doesn't seek a pat on the back for a job well done, but instead fights to ensure that Salem is a thriving city where we can all grow and flourish. She creates a safe haven for those belonging to the LGBTQ+ community (and other racial and ethnic minorities) and provides a sense of safety and affirmation to those who need it most. She has listened to harsh criticism from some residents and has received misogynistic comments from other mayoral candidates or Councillors, comments that wouldn't ever make their way into a political race had there been two male candidates running for the corner office. Yet, she persists.
We are proud to go into the trenches with Mayor Driscoll any day of the week and look forward to what she has in store for Salem moving ahead. The Rainbow Times ardently stands with Mayor Kim Driscoll and offers our unyielding endorsement for her re-ectlection bid.
Salem Councillors At Large*
Alice Merkl; At-Large City Councillor
Alice has endlessly proven that she is fully vested in Salem and has been for a number of years. Her dedication and work are not only for one specific cause, a particular area of interest nor a certain group of people. She is fully dedicated to a wide variety of initiatives and serves all people with the dignity and respect they deserve.
Alice was endorsed by the Massachusetts Women's Political Caucus PAC and the North Shore Labor Council, an interview that dissects candidates' answers in a very long and timed process that isn't easily won.
She has been active in volunteering efforts for the Mack Park Food Farm, the Community Life Center, Salem's Council on Aging, the Salem Food Pantry, and on neighborhood clean-ups just about every month. In the past, she has lent her voice to LGBTQ+ causes, such as the "Yes On 3 Campaign" to educate students and residents during public forums on trans rights issues. She has taken it upon herself to be knowledgeable, informed, and proactive in combating food insecurity, supporting environmental sustainability, housing for all, and historic preservation advocacy, as key issues she's devoted to. Alice has vowed transparency and responsiveness, something that we can never get enough of in politics.
Alice is loyal and trustworthy. She is clear about where she stands and when she doesn't know the answer, she immerses herself in the topic to be able to fully identify answers and seek solutions that align with human rights and needs. Her volunteer work is a testament to that character and willingness to serve others, something which isn't an easy task. This is Alice's second run and like we did the first time, we fully and wholeheartedly endorse her for At-Large City Councilor. We hope you do too.
Ty Hapworth; At-Large City Councillor
Like several of his colleagues, Councillor Hapworth also stood in support of gender-neutral language in city ordinances and voiced such support, not only by a vote. He directly took on the opposition to it and insisted on updating every word to be gender-inclusive, like many cities have already done in the commonwealth. His point, which was misrepresented by dissenters, was based on changing old paper documentation that through the years has purposely left women and their contributions outside of public life, and attempts to allow young girls to see such a reflection of gender-inclusive awareness and terminology for future generations. The same would apply to trans and non-binary resident inclusion.
Councillor Hapworth is one of the most progressive Councillors on the Council. He's not afraid of his open support to marginalized communities, whether it is Black Lives Matter, Indigenous peoples' rights, LGBTQ+ rights, or women's rights, and stands by his convictions. In recent years, he has spearheaded the rainbow crosswalk painting to create a visible representation of the city's support of the LGBTQ+ community in downtown Salem. He is also the male City Councillor most publicly committed to gender equity. Additionally, Councillor Hapworth has earned the endorsement of the North Shore Labor Council and is committed to workers' rights, environmental justice, affordability in all sectors, smart planning and development, innovative technology, and social justice.
Over his short time on the council, Council Hapworth has earned our trust and the trust of others who've placed their confidence in him. We look forward to seeing how Councillor Hapworth continues to challenge outdated thoughts and ideas to reach innovative solutions and inclusive measures for all residents within city borders. The Rainbow Times wholeheartedly endorses Councillor Hapworth to serve a second term as Councillor At Large.
Conrad Prosniewski; At-Large City Councillor
Councillor Prosniewski is well known in the LGBTQ+ community and to BIPOC (Black, Indigenous, People of Color) because of his consistent record of representing Salemites fairly. He has been able to effectively support a majority of initiatives while still maintaining that fairness as much as possible with all constituents he represents. Prosniewski's service-oriented call was clear the first time he ran for office, after retiring from his post as Captain of the Salem Police Department for 41 years. In that capacity, he was able to experience and listen to many of the problems that Salemites faced through the years.
When he says he wants to continue to work on improving the quality of life of Salemites, he means it for all Salemites, not just some. He has done it before and he has also already done it through his work at the City Council. As a member of the Public Safety Sub-Committee of the Salem Race Equity Task Force, SRETF, Councillor Prosniewski was key in moving forward the body cam recommendation for Police Officers and his input was vital in the Task Force as a whole. He was also endorsed by the North Shore Labor Council, something that also speaks to his commitment to working families and individuals.
Councillor Prosniewski listens and even if he disagrees, he plays by the rules, and not in an underhanded manner. He also doesn't play games and is honest about his stances on issues of human rights and service to others. Likewise, if he makes a mistake, he owns it too. Because of his honorable character and solid track record The Rainbow Times proudly endorses Councillor Prosniewski as one of the At-Large City Councilors this November.
NOTE: *There are 4 seats up for grabs. However, at this time, we cannot offer our full endorsement of a 4th candidate. We are able to honorably mention Fred Norton for the 4th seat based on our research of their commitment to progressive causes. He was the only other At-Large candidate to reach out to be interviewed by The Rainbow Times. Unfortunately, our editorial team did not receive his direct answers to our interview questions by the deadline.
Salem – Ward 1*
Bob McCarthy, City Council (Incumbent)
Bob McCarthy has been a long-standing City Councillor who is progressive, inclusive, and uses a practical approach to ensuring all Salem residents are heard. He's not afraid to voice neither opposition nor agreement and uses thoughtful consideration of issues at hand before casting a vote. His voting record substantiates it. And, he was also endorsed by the North Shore Labor Council this year.
The candidate Councillor McCarthy is running against, based on the research conducted by our team, has not supported inclusive causes and has worked to fight against them instead, which goes against the essence and sense of equity to every human being that this publication stands by. If driving a vehicle that proudly shows an insurrection bumper sticker the reads "Trump 2.0" isn't offensive enough, we don't know what is. Several candidates views on the LGBTQ+ community show a clear picture of what is at stake this November.
Now, more than ever, we need people who are unapologetic in their sense and stances for justice, human rights, inclusion, etc. Bob has continued to show his support of people over establishment, and he is the only candidate that can deliver fairness while upholding the visibility and respect that comes with being in office and holding a seat on the City Council. Councillor McCarthy is undoubtedly that person for Ward 1.
*NOTE: The other candidate running for Ward 1 did not respond to our questions.
Salem – Ward 2
Caroline Watson-Felt, City Council
Although we are unable to offer a full endorsement for Watson-Felt, our editorial team would like to honorably mention her for the Ward 2 Council seat. Unfortunately, we did not receive her responses to the endorsement interview by deadline. However, based on The Rainbow Times' research, Watson-Felt is the progressive choice for Ward 2 and is also a member of the LGBTQ+ community.
Patti Morsillo, City Council (Incumbent)
Councillor Morsillo has shown through her consistent voting record that she is not only progressive but that she uplifts the voices of the women of Salem, ensuring they are respected and heard. She has stood up to opposition of progressive causes and has emphatically declared her support and commitment to the LGBTQ+ community, affordable housing, and the pleas of other disenfranchised groups within Salem.
Councillor Morsillo is unabashedly firm in her public stances and has demonstrated the effectiveness of how Councillors should operate. She is a reliable and trustworthy ally with a steady hand that leads the city into the future with conviction. As the incumbent, The Rainbow Times offers the strongest endorsement for Councillor Morsillo to be re-elected to the Ward 3 seat.
Lev McClain, City Council
McClain is a newcomer to City Council politics, but he is not a new resident of Ward 4. A strong communicator online and in person, he has been involved in conversations relevant to issues pertaining to Ward 4 specifically, especially relating to development, infrastructure, the local economy, taxes, and the environment, amongst others. He is a progressive candidate who supports inclusion and sensible development.
A staunch ally of the LGBTQ+ community, he has also received the endorsement of the North Shore Labor Council, an endorsement in itself that is not a simple one to land and which shows his commitment to working-class families and individuals.
As the Associate Director of Security at the Peabody Essex Museum, PEM, McClain understands the importance and place of safety, history, and the arts in the community. As a matter of fact, The Improper Bostonian Magazine selected McClain to feature in an exclusive portrayal of museum security while sharing his favorite works of art. Committed to social justice, McClain has also presented workshops on race equity to help create a broader understanding and inclusive environment for all who enter and work at the PEM.
As a former renter turned homeowner in Ward 4, he recognizes the challenges that residents face pertaining to taxes, rising rent costs, and development. McClain is a humble man with a vision of inclusion and justice for all. He is a stellar communicator and also a Salem school parent who understands the public school system and its needs. He listens closely to the concerns of his prospective constituents while focusing on ways he can collaborate with others to bring the most to the Ward.
In favor of bilingual language education and sensible affordable housing development, McClain has a multitude of experiences with people from all backgrounds, which lends itself to a deeper sense of empathy, comprehension, and relatability to human rights issues. McClain's innate leadership skills far exceed the average candidate. If elected, McClain will make history by becoming the first Black man to be elected to the Salem City Council. We are excited to see McClain fill the Ward 4 city council seat and offer him The Rainbow Times unwavering endorsement.
In contrast, his opponent does just the opposite and is not someone who is open to LGBTQ+ rights or causes, development, and housing solutions, even though she is a renter herself. A fairly new resident to Ward 4, and based on answers given to the Salem Digest, she does not seem to have a clearly defined idea of where she stands or what she aims to do with Ward 4. She was given an opportunity to answer the same questions that McClain was sent but chose not to do so.
*NOTE: In addition to the endorsement interview and research collected about Lev McClain, the publisher of The Rainbow Times, who also was a candidate in the election and got to know the other candidates, offered his personal endorsement of McClain's campaign as well, calling it "honorable, professional and clean." In the spirit of transparency, the publisher did not weigh in on the publication's independent endorsement process.
Jeff Cohen, City Council
Again this year, The Rainbow Times is proud to throw its full endorsement to Jeff Cohen for Ward 5. Cohen has been involved in city initiatives for a number of years serving as Salem's No Place for Hate Chair and Co-chair and as a Board of Directors for Project Out, Inc. As Vice-Chair of the Sustainability, Energy and Resiliency Committee, Cohen was responsible in large part for drafting the Green Building Ordinance as a measure to help avert the climate crisis. He holds a plethora of environmental knowledge that is of the highest integrity. He is proactive and inclusive with all that he does and sticks to his word. Community members often seek Cohen's input on city measures, concerns or questions pertaining to municipal functions or actions as he is immersed in Salem government. He embodies a wealth of knowledge and has extensive experience in advocating for environmental justice, social justice and accessibility issues.
A homeowner in Ward 5 and long-time resident, Cohen plays a critical role in ensuring neighbors and city residents are kept abreast of key information pertaining to city issues. Cohen is a true progressive that has always invested his time, energy, and efforts to improve the lives of those that surround him. He is compassionate, empathetic, and a social justice warrior who will go to bat with anyone that needs him to do so.
Cohen's logic is sound and he acts with determined conviction. He is open about where he stands pertaining human rights issues and has been a vocal supporter of the LGBTQ+ community and other marginalized groups in Salem. The residents of Ward 5 will do well with Cohen as their Councillor and the city would undeniably be fortunate to have him in the Ward 5 seat.
*NOTE: The other candidate running for Ward 5, Steve Kapantis, did not submit his answers on time, although he expressed interest in doing so several times, unfortunately after the deadline had already passed. He was one of two candidates contacted that tried to get them in and for that we are grateful. It shows that he cared enough to get back to this publication and that is worth mentioning.
Meg Riccardi, City Council (Incumbent)
The current incumbent, Councillor Meg Riccardi has demonstrated what exceptional leadership should look like on the Council. She has been unwavering in her support and knowledge of marginalized communities' issues and, when in doubt, she informs herself from experts in the area. Every vote she has made on the Council has been well-thought-out and comes from a fact-based driven perspective. Serving as a member of Salem's Race Equity Task Force, SRETF, Riccardi was fully supportive of inclusive measures proposed by members of marginalized communities themselves, especially the Latinx and LGBTQ+ leaders she worked with directly.
In addition, she has proven to be knowledgeable on issues of injustice and has spoken in council meetings on the importance of inclusion. She was the only Councilor that voiced concern about the timing of an award presented to the SPD, put forth by Councillor Flynn the day after Breonna Taylor's grand jury decision, which was extremely painful to the BIPOC community. In positions of power, it is crucial to be able to act with critical thinking skills, to be able to recognize and empathize with other people's struggles and to be conscientious of what messages are being sent to marginalized communities from elected officials. While Councillor Riccardi fully supported the effort to recognize SPD's work, she knew it was not the right moment to do so as millions of people across the country, and here at home, were rising up in mass protest against systemic abuse and police brutality. We couldn't agree more with her assessment.
Councillor Riccardi is a person of her word, someone residents can trust and who moves and votes to uphold policies that support inclusionary practices in city ordinances, resolutions, and daily concerns like housing, the environment, development, and infrastructure. Based on her statements, interviews with The Rainbow Times, city council votes, and community involvement, Councillor Riccardi has more than earned another term to serve the residents of Ward 6 well. We are thrilled to throw our full support and endorsement behind her again this election cycle.
Andy Varela, City Council
Andy Varela is running for the second time in Ward 7 to replace the seat left vacant by Councillor Steve Dibble who chose to throw his hat into the Mayoral race instead. In stark contrast with the current councillor, Varela would be a refreshing change to the often contentious seat.
As a local farmer, a parent and business owner, Varella understands the importance of nourishing the community at every level. He has placed an emphasis on the preservation and enhancement of the arts, is dedicated to ensure equity and social justice for residents, and is innovative in his approach toward housing and ideas to support families. Additionally, he stands strongly with resiliency efforts as the city continues to look toward a greener future while still developing viable solutions in favor of affordability to help combat the housing crisis, a critical need for Salem residents. Likewise, he has publicly stated his commitment to ages across the spectrum and understands the need to rise to the occasion to meet the challenges faced by young families and seniors alike.
Most importantly, Ward 7 needs a Councillor with a grounded, problem-solving approach and an ability to work in tandem with others from various backgrounds, being guided by a sense of duty and responsibility to serve some of the most vulnerable residents in the city and create an inclusive ward. Division should not be the name of the game in the people's seat and Ward 7 deserves to have a Councillor committed to representing the needs of the majority of residents from informed perspectives and producing fact-driven inclusive results. Andy Varela is that person for Ward 7 and The Rainbow Times is proud to offer our full endorsement of his candidacy.
Lynn City Council – Ward 3
Constantino "Coco" Alinsug
Currently leading the race for Lynn's Ward 3 Council seat, Coco Alinsug has been a lifelong LGBTQ+ champion hero, locally, and abroad in his native Philippines. Also a member of the LGBTQ+ community, Coco has dedicated his life to social justice, representing some of the most marginalized communities around the globe. The Rainbow Times has witnessed Coco's dedication, resiliency, drive, motivation and boundless energy for more than a decade's worth of directly collaborating with him on various causes and initiatives. As we've also witnessed from the first-time candidate this election cycle, the way he has run his campaign is equally as impressive as his resume.
Coco has spent a lifetime also devoting himself to HIV/AIDS prevention, LGBTQ+ youth and the arts and has received countless awards and recognition honoring him for his relentless work to truth and justice, breaking down barriers one person at a time, including being recognized by The Rainbow Times a number of years ago for his honorable work and commitment to the betterment of the LGBTQ+ community. He is a hero to many, especially those often left without a voice and that are persecuted and stigmatized in society.
Most recently during the COVID-19 pandemic, Coco traveled nationally and internationally, educating others about LGBTQ+ health and vaccine research. He is also hailed as one of the original members of the "Protocol Team" that reviewed the study design of the Moderna Covid-19 Vaccine. Additionally, he Though impressive, these factoids just touch the tip of the iceberg.
Coco spent over a decade building and spearheading the Salem-based North Shore Alliance of LGBTQ+ Youth (nAGLY) as the organization's Executive Director and has been, in large part, responsible for the tremendous growth of the organization in its earlier days. Over the past several years in his position as a Commissioner for the Masachusetts LGBTQ+ Youth Commission, which establishes effective policies, programs, and resources for LGBTQ youth throughout the Commonwealth, and as Outreach Manager for Fenway Health, Coco has helped to safe lives, quite literally. He also serves on multiple boards of directors, groups, and community organizations ranging from culture to the arts to community television.
Coco is a leader that throws his heart into all he does. He is not about smoke and mirrors but leads by his own example with conviction, passion, empathy and brilliance. In the years of endorsing candidates for office, our team has never witnessed a Lynn candidate that has thrown themselves into a race with as much vigor, sheer grit and fortitude as Coco. This speaks volumes to the type of person he is and the kind of determined leader he will be as a City Councillor. Coco knows from his personal experience as a gay man, a member of the BIPOC community and through his unmatched social justice-related and management expereience what it takes to persevere and truly serve others.
He has been able to garner palpable energy, support and excitement across the board about his campaign from those who believe in his abilities as much as his person. We join them. It is rare for a candidate to be equally strong as a well-rounded progressive candidate as they are a personal human rights warrior. Yet, Coco checks all the right boxes while coloring outside the lines. If elected, Coco will be the first Fillipino-American and openly gay man elected to Lynn City Council. The Rainbow Times is excited to throw our ardent endorsement behind Coco Alinsug for Ward 3.
Final Thoughts this Season
Although representation of all marginalized groups is critical to local government, equally important are the fundamental beliefs and practices of individual vantage points which will ultimately influence decision making and the votes cast on behalf of constituents. Where candidates stand on issues overall will continue to either advance or halt the progress of what others are able to achieve in city government and for the residents that are affected by it. We are confident in The Rainbow Times' process and to our endorsements above. We fervently stand by them. Vote on November 2.
***Note: The Boston Mayoral Endorsement will be released soon.***
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1 Comment on "Rainbow Times Releases Key Endorsements"
Alan Hanscom | October 25, 2021 at 9:38 pm |
I'm very grateful for this article, but I think that the names of the homophobic/transphobic candidates need to be released. What if I accidentally vote for one of them, and find out later they are against my very existence?


So. I haven't really played anything new, as of late. Pokemon's two weeks away. Why not take this opportunity to talk about a game that's well over a year old? And since we're waiting for Sun & Moon to hit the shelves, why not talk Nintendo? So. Let's dive into Fire Emblem: Fates from the mind of a writer. Let's get into some Scripted Gaming.
Revelations is an interesting little thing. Just to put this into perspective, I've played zero Fire Emblem games before this. The interest just wasn't there. I may play Awakening at some point… may. But I wouldn't hold my breath. I digress. With that being said, I wasn't familiar with the franchise's method of telling its story. And now that I've played through it… about 6 times, I can say that it gets the job done. Not much else, though. I… really doubt anyone plays these for the rich story. Or at least not this one.
No. Stop that. Bad. You play as Corrin. You know. That character with the absurdly unfair upward counter in Smash Bros.? And yet they felt it was Bayonetta's counter that needed nerfing… well, whatever. Technically, you can name them whatever you want, but their "canon" name is Corrin. So we'll just go with that, for now. They've lived most of their life sealed away in this tower in the pretty dismal kingdom of Nohr. Come to find out, though, that they're actually a part of the royal family of a nation that Nohr is at war with – Hoshido. So yeah. These places are respectively Japan and… France? Russia? England? They're East and West, all right? So yeah. Corrin is caught in the middle of all this when her original family gets her back but the escalating conflict between both nations causes her (the first Corrin I made was female, so I'll just refer to them as 'her' for the duration of this) to have to choose a side. Or, if you're playing Revelation, you don't. You choose not to take sides. Of course you do this in what may be the dumbest way possible. You decide that the best course of action is to attack everyone. But that's being unfair. Because, in fairness, the two sides have no intention of listening to reason, anyway. The most likely of the eight siblings to listen to reason are the littlest sisters, and… the odds of them diffusing the situation are just plain nonexistent. So yeah. War, war, fighting, war, aaand you're forced to retreat.
So you wind up learning about this world that you can't tell anyone about and, oh. I forgot to mention this. Corrin's a dragon. This is, surprisingly, not important in any way unless you invest in more DLC to get some backstory. How do I know this? After it's introduced, it serves pretty much no purpose outside of combat. It's never seen in the story, again. And it's not even that amazing in combat, either. You're better off just using Corrin's main weapon in most cases. Though it does have the benefit of essentially turning Corrin into a wall. So yeah. Secret world, can't talk about it, etcetera, etcetera. Corrin wants to find a peaceful solution to ending the war, which is convenient because both sides of the war are actually being manipulated by an ancient evil dragon in this hidden world. So all she needs is to convince both sides to stop fighting, and help her. Clearly easier said than done, right? Actually, no, it's rather easily done. Most of the characters end up joining you after one or two encounters. The eldest brothers give you the most trouble, purely because they're both stubborn as mules.
So. You have everyone on your side, now. Let's go slay us a dragon. Except… not quite. First we have to get there. Getting there is honestly where most of the game's challenge comes from, as this is around when enemies become… well… remotely competent. As for the story? It's… I'll be honest, the story around this point just kind of devolves. Without the war still happening, they were scrambling to add conflict to the thing, and wound up doing so in incredibly haphazard, convoluted ways.
Let's talk about Gunter, shall we? Spoiler alert. Gunter's a traitor. Except he isn't. He isn't even dead. He's just being mind controlled by the main antagonist of the game. How? God knows. But here's a better question… if he can manipulate Gunter, who is still alive, why can he not manipulate… anyone else in the group? What keeps him from just taking over Corrin and screwing everyone over? Okay. Maybe Corrin is protected by… um… hm… okay, DLC spoiler? Corrin is kind of his daughter…sort of. So… maybe that's why? No idea. But he could still, in theory, manipulate anyone else in the group. For all we know, he can manipulate the entire group. What did he decide to do? He decided to manipulate Gunter and use Gunter to shatter Corrin's faith in people by eventually having him betray her. Except… um… that's totally not what he intended to do. His first traitor-y action, using Gunter, was to try to kill her at a point where they couldn't even tell it was Gunter who did it. The result? Scarlet dies in Corrin's place. And don't worry. We'll get back to that. O' we will freaking get back to that. Because I have words about that. So yeah. The Gunter reveal doesn't work. At all. It's made no better by his manipulating the spirits of Arete (Azura's mother), Mikoto (Corrin's mother), and Sumeragi (the father of the Hoshidan siblings). His plan was, most definitely, to kill Corrin. Perhaps he was just over reaching and trying to make it seem poetic or something, by having someone close be the killer, as he felt betrayed by men because they stopped worshipping him, or something? But… that doesn't exactly work when your targets are wholly aware the betrayers are being controlled in some fashion. Thus there is no real wrestling with that doubt. They know they'll likely be betrayed, but also that it isn't of their own choosing. Kinda minimizes the issue, there, Mr. Evil. All it ends up doing is make the entire Gunter arc seem utterly pointless.
You wanna know how to handle betrayal? Let's just revisit Tales of Symphonia, again. Just… go with me on this for a minute. For anyone who's played it, remember when Kratos all but literally stabs you in the back? Didn't see it comin', did ya? Or when Zelos betrays you? Okay, that one's a bit different, but still. Both of those instances were handled infinitely better than this. Because, first of all, no one was being mind-controlled. They were all acting of their own volition, based on past events that shaped their perspectives. And even if they were being mind-controlled, that's a detail you save for the end. You don't blow that card too quickly, or it diminishes the effect. The resolution of Gunter's arc actually reveals he had plenty of genuine motivation to do what he was doing, so why couldn't they just let him do this of his own volition? Play the mind control card to mess with people's expectations and then, "Surprise! This one's not being mind controlled. He's just that far gone!" (I would also like to point out that the Gunter fight was way too easy. Kratos is ashamed).
So you beat Gunter, you fight big evil dragon antagonist. After you beat the crap out of him with your Fire Emblem (aka your sword), he becomes super evil dragon antagonist. Because heaven forbid a JRPG only require you to kill a boss once. Sadly, though, this fight is actually easier than the previous one. Less enemies, more open terrain, and if you played the game right, everyone's leveled to the point where they can tank a hit or two from the fairly heavy-hitting boss. Not to mention that you'll know how to go a few turns without taking any damage at all. Ryoma is surprisingly good for that, thanks to Astra. So yay. You beat the baddie, and one incredibly anticlimactic ending later, you're crowned the ruler of the hidden kingdom (we'll get back to that, too), and the siblings promise to play nice from now on.
Okay. Let's just address this. The Support system of this thing is… it's… it's a mess. Like… a legitimate mess. Now don't get me wrong. It's fun. And it isn't a total train wreck as many characters are just fine. But… they clearly didn't think through a lot of this. I can see very clear areas where they applied more effort to certain routes than others. I feel like when they did this, they thought about it more from a formula standpoint than anything. As if they were just checking boxes on a list. Now. This isn't a problem at all, where it concerns the adult characters. Well… Nyx is a bit problematic because they don't state how old she is, physically, so… that's of some serious concern… Elise and Sakura as well… now that I think of it… even S Supporting just one pair of royals makes the rest of them in-laws, and you can still… wow. This system has more holes than I initially thought about. But whatever. No, the issue lies more with the offspring. See… there are a few holes in this. If you manipulate the Support trees without paying attention to what you're doing, you end up causing S Supports between cousins. Which is… icky, to say the least.
I've come across two defenses for this that people seem to think makes that okay.
Yeah… we'll get to that.
Okay. Yes. That WAS okay in medieval times… in the real world. Problem. The real world doesn't have magic and dragon and werewolves and kitsune, and… do you see where I'm going with this? This is a fictional universe. A universe in which you are entirely free to determine the rules of society. Therefor you chose to make that a thing that was okay. Furthermore, if we're really going to get into "But it's true to the era!" then you can't just use that to defend this without using it to call bull on all the crap from that era that the game just outright ignores. No. That doesn't work with me. Sorry.
So back to half-arsed defense #1… yeah. Technically none of these supports are canon. Except there are 3 reasons that's not an excuse.
That doesn't make it okay. It's still there.
They clearly exhibited knowledge of the concern. How do I know this? Because Midori and Asugi are cousins, canonically. There's nothing you can do about them being cousins. Their dads are brothers. So what did they do? At least in the game's English dub, the dialogue is written as to not even have any romantic implications, let alone full realizations. Now. If I recall correctly this isn't in the Japanese version of the game. Which means that the English dub of the game went to the extra effort to tweak that. In other words, there was absolutely nothing stopping them from doing that with the other characters. All that would have been needed was the extra coding to make the game smart enough to tell who the kid's parents were. And I obviously don't mean that to say coding is a fast or easy process. I get it. But come on. (This is just kind of an afterthought while on the subject, by the way, but why is it, exactly, that none of the royals have daughters? Excluding the princesses, who only have whatever offspring their spouses have… and yes, I know that's a gender thing, flipped from the last game, but… that doesn't dismiss the question).
You can S Support Corrin and Azura. Guess what. They're cousins too. Canonically. Revealed very sloppily towards the end of Revelation. And it honestly affects jack all. The only thing it does is make it so Azura can crown Corrin the ruler of the hidden kingdom. That is literally the only reason for it. And not only is that canon, but the game seems to what that support, itself, to be canon, as well. Which is… what was the word I used before? Ah. Right. Icky. So… so icky.
And that's really just one problem with the Supports. Please don't get me started on the oddity that is Soleil. Because… I can't even deal when it comes to her. She's just a bloody conundrum. They totally wanted her to be anything but straight. And… I guess they tried? Kudos to them? But… her S Supports kind of all throw that out the window, so… granted, all but the ones with Forrest and male Corrin seem to imply just everlasting friendship. Which is fine. But… there's not a single female S Support option for her. Doesn't quite work if ya don't commit, guys. Meanwhile a female Corrin can S Support with Rhajat… can we just… can we be done talking about this? It hurts my brain, trying to figure out how they came up with any of this.
In terms of side characters, most of 'em are fun. Some were annoying at times, but that was intentional at least some of the time. Azama, in particular, quite honestly bugged the crap out of me more often than not. He got a few laughs but his whole outlook just irritated me, at times. And while I love Velouria, at times she was a bit too blunt. Though if I'm honest, I think there is issue to be had. For the better characters in the bunch, their Supports revealed nice bits of background that let you see how they tick and what makes them do the things they do. Most of the royals got this treatment. Nyx, Severa, Inigo, Owain, Peri, Charlotte, Beruka, Niles, the majority of the offspring, and a few other characters. It also made it more interesting, reading some of the subtext, or looking into their actions. Other characters were just fun, like Selkie, Setsuna, and Arthur. Also… Dwyer is my spirit animal. Seriously. The snark. My god, the snark. But there are some characters who were a bit… lacking. I'll focus on Oboro since she was the one that kinda disappointed me. Oboro… is a likeable character. But she also pretty one-note. And by that I mean that in nearly all of her supports they wring the "my parents are dead!" towel so dry it can qualify as sandpaper. And again. She's one I like. She's funny, nice, and actually surprisingly useful throughout the game. But that's… that's basically it for her. Every aspect of her character goes back to that one thing. All of it. She's not really the worst example, though. If we're honest, Kaden may well be the worst offender, as there's no background on him at all. He's a charming character, I guess? But honestly he's pretty forgettable in the grand scheme of things. If not for the fact that he spawns what is easily my favorite character in the game (Selkie! So adorable!) I swear I'd forget he was even in it.
Corrin, by far, won the lottery on this one. Not only does the gender actually somewhat influence their personality, but sheer exposure to the plot allows Corrin the time to really develop. You get to see more and more of the person that their upbringing ultimately led them to become as they're thrown into these new situations and are forced to make decisions. Meanwhile, these situations never lead them to compromise who they are. It explores how someone who came up in that environment might react to things. It comes across in everything from their hobbies, mentioned in support conversations, to their actions in the actual plot of the game. So kudos to them for that.
Overall, it's a fun game, and I like it. Some problems in localization (lordy, the typos), some holes in the final act and Support system, and a few uninspiring characters hold it back a little. There's some laziness going on in the storytelling, but also some funny moments, and solid main character to follow. Could my introduction to this franchise have been stronger? Probably, yeah. From what I've heard, I really should've played the Ike games first. But, eh. C'est la vie. Now if you'll excuse me, I'm gonna go back to waiting on Sun & Moon. Thanks, as always, for reading.


Two Coventry-born poets, Jane Commane and Peter Raynard are to perform in the twin-city of Cork, Republic of Ireland as part of the ongoing poetry exchange now entering its 9th year.
As a continued expression of solidarity and a united commitment to art, the Cov-Cork Poetry Exchange supports emerging and established poets at key points in their artistic career to give two readings in Cork and Clonakilty [August 6-8th]. The poets will be hosted by Paul Casey of O Bheal Poetry, and will receive the same warm and generous welcome that has made the exchange so successful.
The event was supported for many years by Coventry poet, Antony Owen who gave poets the chance to stretch their legs across the water and build upon Coventry's long-standing relationship of friendship and goodwill with its sister city of Cork.
Paul Casey, of Ó Bhéal, said: "Here we mark the occasion of the ninth year of poetry exchanges between Cork and Coventry. Over the years poets from both cities have taken part and formed long-term friendships and meaningful, collaborations.
In November [the 7th – 9th ], two Cork poets will visit Coventry and perform at Coventry's long-established Fire & Dust poetry night, visit the region, perform on local radio and meet with Coventry's Lord Mayor – further embedding the cultural links with our Irish cousins.
Peter Raynard is the editor of Proletarian Poetry (www.proletarianpoetry.com), which has featured over 130 poets on working class lives. He has written two books of poetry: his debut collection Precarious (Smokestack Books, 2018) and The Combination: a poetic coupling of the Communist Manifesto (Culture Matters, 2018). He was sent from Coventry after thirty years, spent ten years in London, and now lives in St Albans, thus is slowly making his way home.


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Ospino è un comune del Venezuela situato nello Stato di Portuguesa.

Il capoluogo del comune è la città di Ospino.

Altri progetti

Collegamenti esterni

Comuni del Portuguesa

redpajama_set_name: RedPajamaWikipedia


This post is sponsored by La Dimora Degli Angeli, thank you for supporting The Wise Willow!
As many of you know, I have been studying Italian for the past year in hopes to return to Italy one day. My family is originally from Italy, and we took a trip there for the first time in the summer of 2015. We visited many cities and towns in Northern Italy, and I have always kept Florence on my bucket list for when I return.
One of the important things to consider when visiting a new place is where you stay–and I have found that I absolutely love Bed and Breakfasts! The La Dimora Degli Angeli B&B has two locations in the historic city centre (La Dimora del Centro and La Dimora degli Angeli). Both locations are close to the Santa Maria Novella train station, which is perfect for exploring new places! The rooms have views of the Duomo in Florence, and are completely furnished with free wifi as part of your stay. They're also air conditioned (which is key for warmer months!), have en-suite bathrooms, secure rooms, double rooms, satellite TV, an in-room phone, and breakfast.
After a long day of walking and exploring the city, returning to one of the amazing room options (there are various to meet your specific needs-whether you are traveling on your own or in a group) is a great way to rest up and relax.
You can find out more information about the two locations (to choose the one that best fits your travel needs and interests–though it might be hard to choose because both are in beautiful locations!) by visiting their site here. You can also learn more about the travel offers that they have available for different times of year, which could be helpful for deciding when you would like to visit!
If you are interested in learning more about what there is to do in the beautiful city, you can visit their blog where there are posts about local events and places to see! Whether you're interested in artwork, local events, or food, there are recommendations that will be a perfect match and information about how to get there.
The locations are non-smoking and also have elevators. There are relaxing tea rooms as well where you can read and enjoy downtime during your day.
Have you visited Florence before? What would you recommend to others looking to travel there soon? Let me know in the comments!


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Home Cover Story Two new Native women elected to Minnesota Legislature
Two new Native women elected to Minnesota Legislature
By Lee Egerstrom
Families that have long been active in community affairs, and inspiration drawn from other take-charge local leaders, have paved the way for two new Native American women to get elected to the Minnesota Legislature.
Rep. Jamie Becker-Finn, an attorney who grew up at Cass Lake on the Leech Lake Band of Ojibwe reservation, won the District 42B seat in the Minnesota House of Representatives. She represents Little Canada, Vadnais Heights, Gem Lake and parts of the cities of Roseville and Shoreview in the northern suburbs of St. Paul.
Rep. Mary Kelly Kunesh-Podein, a library media specialist for Robbinsdale Area Schools, won a House District 41B seat and represents Columbia Heights, Hilltop, New Brighton and St. Anthony in the northern suburbs of Minneapolis and St. Paul. She descends from the Standing Rock Sioux Tribe in North Dakota but grew up in Sartell where her father was a St. Cloud city attorney, an assistant Stearns County attorney, and active legal consultant for Northern Minnesota Ojibwe tribes.
Those nearby and extended examples of family leadership influenced Kunesh-Podein, and she's followed the same path. She has 21 years as a library specialist for schools in Minneapolis and Robbinsdale, and more recently she also became chair of New Brighton Parks, Recreation and Environmental Commission, and this past summer she started the first New Brighton Farmers Market.
This activism continues into the next generation. One daughter, Elianne Farhat, works on fair wages and workplace issues for the Center for Popular Democracy and a son, Elie Farhat, is an assistant to Hennepin County Commissioner Marion Greene.
For her part, Becker-Finn said, "My parents have always been involved in politics so I grew up looking up to people like (the late) Senator Paul Wellstone."
"In recent years, I've seen politics at the state level become extremely partisan and it's turned folks away from even wanting to be involved," she added. I believe what Senator Wellstone believed – that politics, at its best, is about people. And about hope."
Personal experiences clearly influence the two lawmakers' agendas. Assistance for families and protection of the environment are examples.
Kunesh-Podein, who has a bachelor's degree in elementary education from the University of St. Catherine and a master's in information media from St. Cloud State University, was a single mom during a federal government shutdown that prevented her from getting a teaching license. "My pride took a hit when I went to use food stamps and MN Care, but I remembered my dad telling me that those safety nets are there to help us when we need it and I am so thankful for them," she said.
That had a lasting impact. "I felt the anguish of discouragement, but I also learned the courage to pursue my dreams," she said.
As a "life-long learner" from being a parent and an educator, she said she's dedicated to support policies for quality education from pre-kindergarten to post-secondary. Native students, or instance, have low graduation rates in Minnesota and the disparities for Native and Black communities in the state are growing.
Environmental issues also attract her attention. Along with her work on Parks, Rec and Environment in New Brighton, her husband Tim Podein is an active sports fan and outsdoorsman, she said.
The first bill introduced by Becker-Finn, who was a Roseville Parks and Recreation commissioner, could be described as taking care of business for her district. It was a road and bridge bonding bill for a project. But another issue that holds her attention as both a Native and as a state representative is projection of water.
"My district has 14 lakes and a lot of people want those lakes to remain swimmable and fishable," she said.
The problems with water in Flint, Mich. Is on the "minds of many," she said. "I am fortunate to serve on the Environment and Natural Resources Committee and it has been clear from day one that we need strong voices keeping clean water at the forefront."
Becker-Finn made headlines as a Native parent, it should be noted, before she actively started seeking a legislative seat at the State Capitol. She went after store managers who were selling stereotypical and insensitive clothing and costumes for Halloween in 2015. She was shopping for Halloween costumes; she and husband Gabe have two young children.
A particularly solid article on the controversy was provided by Michael Rietmulder in the Oct. 30, 2015 issue of City Pages. One store did remove a particularly offensive sexy costume, she said, but other plastic insults to Native culture and religion stayed on the shelves.
She was too busy campaigning at Halloween time this year to revisit the suburban stores. But friends told her all the offensive gear was back. "There is definitely a lot of work to be done, as you can see with the Washington Redskins and Cleveland 'Indians'."
Native people are everywhere, she said, including in the Minnesota House of Representatives. And, she added, "We don't always look like the caricatures you see on ESPN."
american indans
Jamie Becker-Finn
Mary Kelly Kunesh-Podein
minnesota american indians
native american women
Native politicians
native women
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If you have a physical tremor which results in shaky hands it can be hard to shave and get a good finish, whilst also avoid getting shaving cuts and other damage when using a normal razor. Here are some other options for hair removal.
If you have trouble with hand stability it can often be easier to apply depilatory cream to the area that you are treating. This application requires less precision and can be much easier to deal with. If you make any errors with the application, it is also easy to remove the cream and avoid removing the hair from that area, whilst errors made when shaving are permanent (at least until the hair grows back!). Some people have issues with skin sensitivity when using depilatory cream so it can be worth looking for a sensitive skin formulation if you tend to have issues with skin irritation.
Waxing can be another great option as it gives a longer hair free finish and there is some flexibility in time to work the wax after application to get the right shape after application. If you find it hard to apply the wax you can ask a friend or head into a beauty salon to get the correct shape formed. It can be a little painful for some people but getting professional application tends to be a little less painful as the beauty therapist can hold the skin firmly when removing the wax.
Finally, if the hair removal is a constant and ongoing issue for you, you can look to get permanent hair removal such as laser hair removal. This can be expensive but can be viewed as an investment. This hair removal uses light waves to permanently remove or reduce the amount of hair so can be very useful if you have hair that you always want to be removed (ie not a mustache or beard where you might be looking to change the style of the hair over time). This is performed by a therapist in a beauty salon or medical centre.
If you are heading to a beauty salon for waxing or permanent hair removal it is a good idea to warn them that you suffer from tremors so that they can modify any procedures to allow for your issues. A skilled technician can work around this constraint to get you a perfect, hair free finish.


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331785 Sumners è un asteroide della fascia principale. Scoperto nel 2003, presenta un'orbita caratterizzata da un semiasse maggiore pari a  e da un'eccentricità di 0,4317462, inclinata di 25,40767° rispetto all'eclittica.

L'asteroide è dedicato a Carolyn Sumners, divulgatrice in campo astronomico presso il planetario del museo di scienze naturali di Houston.

Collegamenti esterni

Sumners
Corpi celesti scoperti nel 2003


The movie playing, inside the city's largest theater, was nearing climax. The protagonist and the villain were engaged in confrontation. People were cheering the protagonist. Suddenly a loud sound of explosion came from the front. The cinema stopped. Momentary silence descended on the cinema hall. Then came the cries and yells from the crowd. Panic engulfed everywhere. Bodies of the dead seemed like islands amidst the blood strewn all around. Ram, a doctor, felt that he would be of help to the injured. He asked his wife to go back home. She, though not in a mood to leave him behind, respected Ram's decision and decided to leave. There was commotion near the exit. There were people shouting at each other. It was a mad scramble to save one's own life. Amidst the chaos, tragedy struck again. Another explosion near the exit. More blood, more bodies and more mayhem. Anxious about his beloved, Ram, caught in the midst of bruised and critically ill, could not help but rush to the door . To his unimaginable horror, he realised that terror had ended his thirty day old marriage life. The magnitude of the cataclysm was so huge that it transcended every form of expression of pain. Movies end. But here, not just the movie, the life of his love too came to an end.
Dreams of a beautiful life to be lived were shattered by those who had death in their minds.
It was post-terror-attack-morning, as usual, the next day. Newspapers, politicians, 'intellectuals' condemned the attacks as ever. They, as is the tradition, asked everyone to maintain communal harmony. Police was under pressure to nab the terrorists. Next day they released computer generated images of the suspected terrorists Nadim and Salim. The faces were shockingly familiar to Suhas, Ram's friend. Feigning themselves as engineering students, they had deceived Suhas to rent his house to them. He immediately called Ram and told him about this. Off they rushed to the police station. Suhas told whatever he knew about them to the police.
A fortnight passed. The two terrorists were caught. Sufficient evidence surfaced against the suspects. Their links with terror organizations, their radical leanings, and their elaborate plan of attack were thoroughly brought out through investigation by the police.
The pace with which the police moved in this case rattled the media. 'Police torturing innocent students' screamed the newspapers and television news channels. There were protest rallies led by human rights activist Ms. Ratnakar. Though sparsely attended, these rallies were described by the media as huge. 'Is our police justified in harassing minorities under the pretense of fighting terror?' asked Mr. Desai, a leading television news anchor, in a tone so shrill that it would have put off the bats in the vicinity that night. Watching this, an otherwise calm person, Ram burst out angrily. In his rage he smashed his television. Suhas, who was then beside Ram, was moved by this magnitude of helplessness of a terror victim. Suhas' eyes went moist, but the moisture glistened in the ray of determination that became visible in his eyes. He made up his mind to organise people and stage a counter protest rally. People came in large numbers. Media condemned it as interference in the 'due course of law'.
But the wheels of justice moved forward unperturbed. The case moved to the courts. The prosecution argued their case diligently. Soon the judgment day arrived. "The two men, Nadim and Salim have been found guilty....This court sentences them to death", came the pronouncement of the judge. Joy that justice had been done, intensely macabre memories of that fateful day and the resulting anger against the murderers filled Ram's mind. Little did he know that the battle was far from over.
The case moved on to the higher court. Verdict remained the same there too. Finally to the supreme court, where too the death sentence was upheld.
'Justice has been unfair', came the media's foul cry. 'Mercy by the President is the only way to soothe assuaged feelings', wrote Ms. Ratnakar in a leading daily. She again hit the road. Violence was manufactured to show, 'the sense of hurt, that was inflicted in the name of religion'. Trivial electoral considerations forced the Government to falter. The convicted terrorists were pardoned.
'Nadim and Salim vindicated', screamed the news channels. Ram, watching this, boiled with anger. The other day there was no expression that could express his pain, today there was no expression that could express his rage, his disgust, his helplessness, his sense of having been denied justice. Memories of his wife swelled up in his mind. He could not save her then from the jaws of death. Now he was unable to see justice done to those who took her life. In his pathos, unable to compose himself, he ended his life.
Few months passed. Another terror strike. This time its prey was the country's home minister. The investigation was high-profile. 'Police arrest Nadim and Salim - main accused in Home Minister's assassination' - read the headlines few days later.
Very bloody. I expected it only to be a paragraph, as it was meant to be short.
[wanderlust]Very much so. In this case,very insipidly.
One paragraph is way too short even for a story as predictable and as thin-plotted as this.
Some extrapolation would have made it nicer, IMO.
I had read this before its publication online and duly commended it and you.
I like HyperWebenables story also.
been through your all writeups here.. Liked your sense of choosing topic and your views. You have superb talent of writing..


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\section{Introduction}\

An edge coloring of a graph $G$ with colors $1,2,\ldots ,t$ is
called an interval $t$-coloring if for each $i\in \{1,2,\ldots,t\}$
there is at least one edge of $G$ colored by $i$, and the colors of
edges incident to any vertex of $G$ are distinct and form an
interval of integers. Interval edge colorings naturally arise in
scheduling problems and are related to the problem of constructing
timetables without \textquotedblleft gaps\textquotedblright for
teachers and classes. The notion of interval edge colorings was
introduced by Asratian and Kamalian \cite{b1} in 1987. In \cite{b1}
they proved that if a triangle-free graph $G=\left(V,E\right)$ has
an interval $t$-coloring, then $t\leq \left\vert V\right\vert -1$.
In \cite{b19} interval edge colorings of complete bipartite graphs
and trees were investigated. Furthermore, Kamalian \cite{b20} showed
that if $G$ admits an interval $t$-coloring, then $t\leq 2\left\vert
V\right\vert -3$. Giaro, Kubale and Malafiejski \cite{b12} proved
that this upper bound can be improved to $2\left\vert V\right\vert
-4$ if $\left\vert V\right\vert \geq 3$. For a planar graph $G$,
Axenovich \cite{b5} showed that if $G$ has an interval $t$-coloring,
then $t\leq \frac{11}{6}\left\vert V\right\vert$. In general, it is
an $NP$-complete problem to decide whether a given bipartite graph
$G$ admits an interval edge coloring \cite{b35}. In papers
\cite{b2,b4,b5,b7,b8,b9,b10,b11,b12,b13,b14,b15,b16,b19,b20,b21,b22,b23,b29,b30,b32,b34}
the problem of existence and construction of interval edge colorings
was considered and some bounds for the number of colors in such
colorings of some classes of graphs were given. Surveys on this
topic can be found in some books \cite{b3,b18,b25}.

The different products of graphs were introduced by Berge \cite{b6},
Sabidussi \cite{b33} and Vizing \cite{b36}. There are many papers
\cite{b17,b24,b26,b27,b28,b31,b38} devoted to edge colorings of
various products of graphs. In this paper we investigate interval
edge colorings of various products of graphs.

\bigskip

\section{Definitions and preliminary results}\

All graphs considered in this paper are finite, undirected and have
no loops or multiple edges. Let $V(G)$ and $E(G)$ denote the sets of
vertices and edges of $G$, respectively. The maximum degree of a
vertex of $G$ is denoted by $\Delta (G)$ and the chromatic index of
$G$ by $\chi ^{\prime }\left( G\right)$. A partial edge coloring of
$G$ is a coloring of some of the edges of $G$ such that no two
adjacent edges receive the same color. If $\alpha $ is a partial
edge coloring of $G$ and $v\in V(G)$ then $S\left( v,\alpha \right)$
denotes the set of colors of colored edges incident to $v$.

A graph $G$ is interval colorable, if there is an integer $t\geq 1$,
for which $G$ has an interval $t$-coloring. Let $\mathfrak{N}$ be
the set of all interval colorable graphs \cite{b1,b20}. For a graph
$G\in \mathfrak{N}$, the least and the greatest values of $t$ for
which $G$ has an interval $t$-coloring are denoted by $w\left(
G\right)$ and $W\left(G\right)$, respectively.

Let $G=(V(G),E(G))$ and $H=(V(H),E(H))$ be two graphs.

The Cartesian product $G\square H$ is defined as follows:
\begin{center}
$V(G\square H)=V(G)\times V(H)$, $E(G\square
H)=\{((u_{1},v_{1}),(u_{2},v_{2}))|$

$u_{1}=u_{2}~and~(v_{1},v_{2})\in E(H)~or~v_{1}=v_{2}~and~
(u_{1},u_{2})\in E(G)\}$.
\end{center}

The tensor (direct) product $G\times H$ is defined as follows:
\begin{center}
$V(G\times H)=V(G)\times V(H)$,

$E(G\times H)=\{((u_{1},v_{1}),(u_{2},v_{2}))|~(u_{1},u_{2})\in
E(G)~and~(v_{1},v_{2})\in E(H)\}$.
\end{center}

The strong tensor (semistrong) product $G\otimes H$ is defined as
follows:
\begin{center}
$V(G\otimes H)=V(G)\times V(H)$, $E(G\otimes
H)=\{((u_{1},v_{1}),(u_{2},v_{2}))|$

$~(u_{1},u_{2})\in E(G)~and~(v_{1},v_{2})\in
E(H)~or~v_{1}=v_{2}~and~(u_{1},u_{2})\in E(G)\}$.
\end{center}

The strong product $G\boxtimes H$ is defined as follows:
\begin{center}
$V(G\boxtimes H)=V(G)\times V(H)$, $E(G\boxtimes
H)=\{((u_{1},v_{1}),(u_{2},v_{2}))|~(u_{1},u_{2})\in E(G)$

$~and~(v_{1},v_{2})\in E(H)~or~u_{1}=u_{2}~and~(v_{1},v_{2})\in
E(H)~or~v_{1}=v_{2}~and~ (u_{1},u_{2})\in E(G)\}$.
\end{center}

The lexicographic product (composition) $G[H]$ is defined as
follows:
\begin{center}
$V(G[H])=V(G)\times V(H)$,

$E(G[H])=\{((u_{1},v_{1}),(u_{2},v_{2}))|~(u_{1},u_{2})\in
E(G)~or~u_{1}=u_{2}~and~(v_{1},v_{2})\in E(H)\}$.
\end{center}

The terms and concepts that we do not define can be found in
\cite{b37}.\\

Asratian and Kamalian proved the following:
\begin{theorem}
\label{mytheorem1}\cite{b1}. Let $G$ be a regular graph. Then

\begin{description}
\item[(1)] $G\in \mathfrak{N}$ if and only if $\chi ^{\prime}(G)=\Delta(G)$.

\item[(2)] If $G\in \mathfrak{N}$ and $\Delta(G)\leq t\leq W(G)$, then $G$
has an interval $t$-coloring.
\end{description}
\end{theorem}

\begin{corollary}
\label{mycorollary1} If $G$ is an $r$-regular bipartite graph, then
$G\in \mathfrak{N}$ and $w(G)=r$.
\end{corollary}

Kubale and Giaro proved the following:
\begin{theorem}
\label{mytheorem2}\cite{b25}. If $G,H\in \mathfrak{N}$, then
$G\square H\in \mathfrak{N}$. Moreover, $w(G\square H)\leq
w(G)+w(H)$ and $W(G\square H)\geq W(G)+W(H)$.
\end{theorem}

The $k$-dimensional grid $G(n_{1},n_{2},\ldots,n_{k})$, $n_{i}\in
\mathbf{N}$ is the Cartesian product of paths $P_{n_{1}}\square
P_{n_{2}}\square \cdots \square P_{n_{k}}$. The cylinder
$C(n_{1},n_{2})$ is the Cartesian product $P_{n_{1}}\square
C_{n_{2}}$ and the torus $T(n_{1},n_{2})$ is the Cartesian product
$C_{n_{1}}\square C_{n_{2}}$, where $C_{n_{i}}$ is the cycle of
length $n_{i}$. For these graphs Kubale and Giaro proved the
following:

\begin{theorem}
\label{mytheorem3}\cite{b10}. If $G=G(n_{1},n_{2},\ldots,n_{k})$ or
$G=C(m,2n)$, $m\in \mathbf{N}$, $n\geq 2$, or $G=T(2m,2n)$, $m,n\geq
2$, then $G\in \mathfrak{N}$ and $w(G)=\Delta (G)$.
\end{theorem}

For the greatest possible number of colors in interval edge
colorings of grid graphs Petrosyan and Karapetyan proved the
following theorems:

\begin{theorem}
\label{mytheorem4}\cite{b29}. If $G=C(m,2n)$, $m\in \mathbf{N}$,
$n\geq 2$, then $W(G)\geq 3m+n-2$.
\end{theorem}

\begin{theorem}
\label{mytheorem5}\cite{b29}. If $G=T(2m,2n)$, $m,n \geq 2$, then
$W(G)\geq \max\{3m+n,3n+m\}$.
\end{theorem}

In \cite{b30} Petrosyan investigated interval edge colorings of
complete graphs and $n$-dimensional cubes $Q_{n}$. In particular, he
proved the following theorems:

\begin{theorem}
\label{mytheorem6} $~W\left(Q_{n}\right)\geq
\frac{n\left(n+1\right)}{2}$ for any $n\in \mathbf{N}$.
\end{theorem}

\begin{theorem}
\label{mytheorem7} Let $n=p2^{q}$, where $p$ is odd and $q$ is
nonnegative. Then
\begin{center}
$W\left(K_{2n}\right)\geq 4n-2-p-q$.
\end{center}
\end{theorem}

The Hamming graph $H(n_{1},n_{2},\ldots,n_{k})$, $n_{i}\in
\mathbf{N}$ is the Cartesian product of complete graphs
$K_{n_{1}}\square K_{n_{2}}\square \cdots \square K_{n_{k}}$. The
graph $H_{n}^{k}$ is the Cartesian product of the complete graph
$K_{n}$ by itself $k$ times. It is easy to see that from Theorems
\ref{mytheorem1}, \ref{mytheorem2} and \ref{mytheorem7}, we have the
following result:

\begin{theorem}
\label{mytheorem8} Let $n=p2^{q}$, where $p$ is odd and $q$ is
nonnegative. Then
\begin{description}
\item[(1)] $H_{2n}^{k}\in \mathfrak{N}$,

\item[(2)] $w(H_{2n}^{k})=(2n-1)k$,

\item[(3)] $W(H_{2n}^{k})\geq (4n-2-p-q)k$.
\end{description}
\end{theorem}

It is known that there are graphs $G$ and $H$ for which $G\square
H\in \mathfrak{N}$ ($G[H]\in \mathfrak{N}$), but $G\in
\mathfrak{N}$, $H\notin\mathfrak{N}$ or $G,H\notin\mathfrak{N}$. For
example, $K_{2}\square C_{3}\in \mathfrak{N}$ and $K_{1,1,3}\square
C_{3}\in \mathfrak{N}$ ($K_{2}[C_{5}]\in \mathfrak{N}$ and
$C_{5}[P]\in \mathfrak{N}$), but $K_{1,1,3},C_{3}\notin
\mathfrak{N}$ ($P,C_{5}\notin \mathfrak{N}$, where $P$ is the
Petersen graph). Moreover, general results can be obtained from the
following theorems:

\begin{theorem}
\label{mytheorem9} (Kotzig \cite{b24}, Pisanski, Shawe-Taylor, Mohar
\cite{b31}) If $G$ and $H$ are two regular graphs for which at least
one of the following conditions holds:

\begin{description}
\item[(1)] $G$ and $H$ contain a perfect matching,

\item[(2)] $\chi^{\prime}(G)=\Delta(G)$,

\item[(3)] $\chi^{\prime}(H)=\Delta(H)$,
\end{description}
then $\chi^{\prime}(G\square H)=\Delta(G\square H)$ and
$\chi^{\prime}(G[H])=\Delta(G[H])$.
\end{theorem}

\begin{theorem}
\label{mytheorem10} (Kotzig \cite{b24}, Pisanski, Shawe-Taylor,
Mohar \cite{b31}) Let $G$ be a cubic graph. Then
$\chi^{\prime}(G\square C_{n})=\Delta(G\square C_{n})=5$ and
$\chi^{\prime}(C_{n}[G])=\Delta(C_{n}[G])$ for any $n\geq 4$.
\end{theorem}

\begin{corollary}
\label{mycorollary2} If $G$ and $H$ are two regular graphs for which
at least one of the following conditions holds:

\begin{description}
\item[(1)] $G$ and $H$ contain a perfect matching,

\item[(2)] $G\in \mathfrak{N}$,

\item[(3)] $H\in \mathfrak{N}$,
\end{description}
then $G\square H,G[H]\in \mathfrak{N}$ and $w(G\square
H)=\Delta(G\square H)$, $w(G[H])=\Delta(G[H])$.
\end{corollary}

\begin{corollary}
\label{mycorollary3} Let $G$ be a cubic graph. Then $G\square
C_{n},C_{n}[G]\in \mathfrak{N}$ and $w(G\square
C_{n})=\Delta(G\square C_{n})=5$, $w(C_{n}[G])=\Delta(C_{n}[G])$ for
any $n\geq 4$.
\end{corollary}

\begin{theorem}
\label{mytheorem11} The torus $T(n_{1},n_{2})\in \mathfrak{N}$ if
$n_{1}\cdot n_{2}$ is even, $T(n_{1},n_{2})\notin \mathfrak{N}$ if
$n_{1}\cdot n_{2}$ is odd and the Hamming graph
$H(n_{1},n_{2},\ldots,n_{k})\in \mathfrak{N}$ if $n_{1}\cdot
n_{2}\cdots n_{k}$ is even, $H(n_{1},n_{2},\ldots,n_{k})\notin
\mathfrak{N}$ if $n_{1}\cdot n_{2}\cdots n_{k}$ is odd.
\end{theorem}

\begin{proof} Since $T(n_{1},n_{2})$ and $H(n_{1},n_{2},\ldots,n_{k})$ are regular graphs,
by Theorem \ref{mytheorem1} and Corollary \ref{mycorollary2}, we
have $T(n_{1},n_{2})\in \mathfrak{N}$ when $n_{1}\cdot n_{2}$ is
even and $H(n_{1},n_{2},\ldots,n_{k})\in \mathfrak{N}$ when
$n_{1}\cdot n_{2}\cdots n_{k}$ is even.

Let us show that $T(n_{1},n_{2})\notin \mathfrak{N}$ when
$n_{1}\cdot n_{2}$ is odd and $H(n_{1},n_{2},\ldots,n_{k})\notin
\mathfrak{N}$ when $n_{1}\cdot n_{2}\cdots n_{k}$ is odd.

Since $T(n_{1},n_{2})$ and $H(n_{1},n_{2},\ldots,n_{k})$ are regular
graphs, we have

\begin{center}
$\vert E(T(n_{1},n_{2}))\vert= 2n_{1}\cdot n_{2}$ and $\vert
E(H(n_{1},n_{2},\ldots,n_{k}))\vert = \frac{n_{1}\cdot n_{2}\cdots
n_{k}\cdot \Delta(H(n_{1},n_{2},\ldots,n_{k}))}{2}$.
\end{center}

If $\chi^{\prime}(T(n_{1},n_{2}))=\Delta(T(n_{1},n_{2}))=4$, then
\begin{center}
$\vert E(T(n_{1},n_{2}))\vert \leq 2(n_{1}\cdot n_{2}-1)$, since
$n_{1}\cdot n_{2}$ is odd.
\end{center}

This shows that
$\chi^{\prime}(T(n_{1},n_{2}))=\Delta(T(n_{1},n_{2}))+1=5$ and, by
Theorem \ref{mytheorem1}, $T(n_{1},n_{2})\notin \mathfrak{N}$.

Similarly, if
$\chi^{\prime}(H(n_{1},n_{2},\ldots,n_{k}))=\Delta(H(n_{1},n_{2},\ldots,n_{k}))$,
then
\begin{center}
$\vert E(H(n_{1},n_{2},\ldots,n_{k}))\vert \leq
\frac{\left(n_{1}\cdot n_{2}\cdots n_{k}-1\right)\cdot
\Delta(H(n_{1},n_{2},\ldots,n_{k}))}{2}$, since $n_{1}\cdot
n_{2}\cdots n_{k}$ is odd.
\end{center}

This shows that
$\chi^{\prime}(H(n_{1},n_{2},\ldots,n_{k}))=\Delta(H(n_{1},n_{2},\ldots,n_{k}))+1$
and, by Theorem \ref{mytheorem1}, $H(n_{1},n_{2},\ldots,n_{k})\notin
\mathfrak{N}$. ~$\square$
\end{proof}

\bigskip

\section{Main results}\

First, we consider interval edge colorings of the tensor product of
graphs. In \cite{b25} Kubale and Giaro noted that there are graphs
$G,H\in \mathfrak{N}$, such that $G\times H\notin \mathfrak{N}$.
Here, we prove that if one of the graphs belongs to $\mathfrak{N}$
and the other is regular, then $G\times H\in \mathfrak{N}$.

\begin{theorem}
\label{mytheorem12} If $G\in \mathfrak{N}$ and $H$ is an $r$-regular
graph, then $G\times H\in \mathfrak{N}$. Moreover, $w(G\times H)\leq
w(G)\cdot r$ and $W(G\times H)\geq W(G)\cdot r$.
\end{theorem}
\begin{proof} Let $V(G)=\{u_{1},u_{2},\ldots,u_{n}\}$,
$V(H)=\{v_{1},v_{2},\ldots,v_{m}\}$ and

\begin{center}
$V\left(G\times H\right)=\left\{w_{j}^{(i)}|~1\leq i\leq n, 1\leq
j\leq m\right\}$,
\end{center}

\begin{center}
$E\left(G\times
H\right)=\left\{\left(w_{p}^{(i)},w_{q}^{(j)}\right)|\left(u_{i},u_{j}\right)\in
E(G)~and~\left(v_{p},v_{q}\right)\in E(H)\right\}$.
\end{center}

Let us consider the graph $K_{2}\times H$. Clearly, $K_{2}\times H$
is an $r$-regular bipartite graph, thus, by Corollary
\ref{mycorollary1}, $K_{2}\times H\in \mathfrak{N}$ and
$w\left(K_{2}\times H\right)=r$. Let $\alpha$ be an interval
$t$-coloring of the graph $G$, $\beta$ be an interval $r$-coloring
of the graph $K_{2}\times H$ and

\begin{center}
$V\left(K_{2}\times
H\right)=\{x_{1},x_{2},\ldots,x_{m},y_{1},y_{2},\ldots,y_{m}\}$,
\end{center}

\begin{center}
$E\left(K_{2}\times
H\right)=\left\{\left(x_{i},y_{j}\right)|\left(v_{i},v_{j}\right)\in
E(H), 1\leq i\leq m,1\leq j\leq m\right\}$.
\end{center}

Define an edge coloring $\gamma$ of the graph $G\times H$ in the
following way:

for every $\left(w_{p}^{(i)},w_{q}^{(j)}\right)\in E(G\times H)$

\begin{center}
$\gamma
\left(\left(w_{p}^{(i)},w_{q}^{(j)}\right)\right)=\left(\alpha
\left(\left(u_{i},u_{j}\right)\right)-1\right)\cdot r+\beta
\left(\left(x_{p},y_{q}\right)\right)$,
\end{center}
where $1\leq i\leq n, 1\leq j\leq n, 1\leq p\leq m, 1\leq q\leq
m$.\\

It is not difficult to see that $\gamma$ is an interval $t\cdot
r$-coloring of the graph $G\times H$. By the definition of $\gamma$,
we have $w(G\times H)\leq w(G)\cdot r$ and $W(G\times H)\geq
W(G)\cdot r$. ~$\square$
\end{proof}

The Figure \ref{example} shows the interval $6$-coloring $\gamma$ of
the graph $P_{4}\times C_{5}$ described in the proof of Theorem
\ref{mytheorem12}.\\

\begin{figure}[h]
\begin{center}
\includegraphics[height=20pc,width=25pc]{fig1.eps}\
\caption{The interval $6$-coloring $\gamma$ of the graph
$P_{4}\times C_{5}$.}\label{example}
\end{center}
\end{figure}

Note that from Theorems \ref{mytheorem1} and  \ref{mytheorem12}, we
have the following result:

\begin{corollary}
\label{mycorollary4} (Pisanski, Shawe-Taylor, Mohar \cite{b31}) If
$G$ is $1$-factorable and $H$ is a regular graph, then $G\times H$
is also $1$-factorable.
\end{corollary}

We showed that if $G\in \mathfrak{N}$ and $H$ is regular, then
$G\times H\in \mathfrak{N}$. Now we prove a similar result for the
strong tensor product of graphs.

\begin{theorem}
\label{mytheorem13} If $G\in \mathfrak{N}$ and $H$ is an $r$-regular
graph, then $G\otimes H\in \mathfrak{N}$. Moreover, $w(G\otimes
H)\leq w(G)\cdot (r+1)$ and $W(G\otimes H)\geq W(G)\cdot (r+1)$.
\end{theorem}
\begin{proof} Let $V(G)=\{u_{1},u_{2},\ldots,u_{n}\}$,
$V(H)=\{v_{1},v_{2},\ldots,v_{m}\}$ and

\begin{center}
$V\left(G\otimes H\right)=\left\{w_{j}^{(i)}|~1\leq i\leq n, 1\leq
j\leq m\right\}$,
\end{center}

\begin{center}
$E\left(G\otimes H\right)=E\left(G\times
H\right)\cup\left\{\left(w_{p}^{(i)},w_{p}^{(j)}\right)|~1\leq p\leq
m~and~\left(u_{i},u_{j}\right)\in E(G)\right\}$.
\end{center}

Let us consider the graph $K_{2}\otimes H$. Clearly, $K_{2}\otimes
H$ is an $(r+1)$-regular bipartite graph, thus, by Corollary
\ref{mycorollary1}, $K_{2}\otimes H\in \mathfrak{N}$ and
$w\left(K_{2}\otimes H\right)=r+1$. Let $\alpha$ be an interval
$t$-coloring of the graph $G$, $\beta$ be an interval
$(r+1)$-coloring of the graph $K_{2}\otimes H$ and

\begin{center}
$V\left(K_{2}\otimes
H\right)=\{x_{1},x_{2},\ldots,x_{m},y_{1},y_{2},\ldots,y_{m}\}$,
\end{center}

\begin{center}
$E\left(K_{2}\otimes H\right)=\left\{\left(x_{i},y_{i}\right)|~1\leq
i\leq m\right\}\cup E\left(K_{2}\times H\right)$.
\end{center}

Define an edge coloring $\gamma$ of the graph $G\otimes H$ in the
following way:

for every $\left(w_{p}^{(i)},w_{q}^{(j)}\right)\in E(G\otimes H)$

\begin{center}
$\gamma
\left(\left(w_{p}^{(i)},w_{q}^{(j)}\right)\right)=\left(\alpha
\left(\left(u_{i},u_{j}\right)\right)-1\right)\cdot (r+1)+\beta
\left(\left(x_{p},y_{q}\right)\right)$,
\end{center}
where $1\leq i\leq n, 1\leq j\leq n, 1\leq p\leq m, 1\leq q\leq
m$.\\

It is not difficult to see that $\gamma$ is an interval $t\cdot
(r+1)$-coloring of the graph $G\otimes H$. By the definition of
$\gamma$, we have $w(G\otimes H)\leq w(G)\cdot (r+1)$ and
$W(G\otimes H)\geq W(G)\cdot (r+1)$. ~$\square$
\end{proof}

The Figure \ref{example1} shows the interval $9$-coloring $\gamma$
of the graph $P_{4}\otimes C_{5}$ described in the proof of Theorem
\ref{mytheorem13}.\\

\begin{figure}[h]
\begin{center}
\includegraphics[height=20pc,width=25pc]{fig2.eps}\
\caption{The interval $9$-coloring $\gamma$ of the graph
$P_{4}\otimes C_{5}$.}\label{example1}
\end{center}
\end{figure}

Note that from Theorems \ref{mytheorem1} and \ref{mytheorem13}, we
have the following result:

\begin{corollary}
\label{mycorollary5} (Pisanski, Shawe-Taylor, Mohar \cite{b31}) If
$G$ is $1$-factorable and $H$ is a regular graph, then $G\otimes H$
is also $1$-factorable.
\end{corollary}

Next, we consider interval edge colorings of the strong product of
graphs. In \cite{b25} Kubale and Giaro noted that there are graphs
$G,H\in \mathfrak{N}$, such that $G\boxtimes H\notin \mathfrak{N}$.
Here, we prove that if two graphs belong to $\mathfrak{N}$ and one
of them is regular, then $G\boxtimes H\in \mathfrak{N}$.

\begin{theorem}
\label{mytheorem14} If $G,H\in \mathfrak{N}$ and $H$ is an
$r$-regular graph, then $G\boxtimes H\in \mathfrak{N}$. Moreover,
$w(G\boxtimes H)\leq w(G)\cdot (r+1)+r$ and $W(G\boxtimes H)\geq
W(G)\cdot (r+1)+r$.
\end{theorem}
\begin{proof} Let $V(G)=\{u_{1},u_{2},\ldots,u_{n}\}$,
$V(H)=\{v_{1},v_{2},\ldots,v_{m}\}$ and

\begin{center}
$V\left(G\boxtimes H\right)=\bigcup_{i=1}^{n}V^{i}(H)$, where
$V^{i}(H)=\left\{w_{j}^{(i)}|~1\leq j\leq m\right\}$,
\end{center}

\begin{center}
$E\left(G\boxtimes H\right)=E\left(G\otimes H\right)\cup
\bigcup_{i=1}^{n}E^{i}(H)$, where
\end{center}

\begin{center}
$E^{i}(H)=\left\{\left(w_{p}^{(i)},w_{q}^{(i)}\right)|~\left(v_{p},v_{q}\right)\in
E(H)\right\}$.
\end{center}

For $i=1,2,\ldots,n$, define a graph $H_{i}$ as follows:
\begin{center}
$H_{i}=\left(V^{i}(H),E^{i}(H)\right)$.
\end{center}

First of all note that $\chi ^{\prime}(H)=\Delta(H)=r$ since $H\in
\mathfrak{N}$ and $H$ is an $r$-regular graph. This implies that
there exists an interval $r$-coloring of the graph $H$. Let us
consider the graph $K_{2}\otimes H$. Clearly, $K_{2}\otimes H$ is an
$(r+1)$-regular bipartite graph, thus, by Corollary
\ref{mycorollary1}, $K_{2}\otimes H\in \mathfrak{N}$ and
$w\left(K_{2}\otimes H\right)=r+1$. Let $\alpha$ be an interval
$t$-coloring of the graph $G$, $\beta$ be an interval
$(r+1)$-coloring of the graph $K_{2}\otimes H$.

Define an edge coloring $\gamma$ of the graph $G\boxtimes H$ in the
following way:

\begin{description}
\item[(1)] for every $\left(w_{p}^{(i)},w_{q}^{(j)}\right)\in E(G\otimes H)$

\begin{center}
$\gamma
\left(\left(w_{p}^{(i)},w_{q}^{(j)}\right)\right)=\left(\alpha
\left(\left(u_{i},u_{j}\right)\right)-1\right)\cdot (r+1)+\beta
\left(\left(x_{p},y_{q}\right)\right)$,
\end{center}
where $1\leq i\leq n, 1\leq j\leq n, 1\leq p\leq m, 1\leq q\leq m$.

\item[(2)] for $i=1,2,\ldots,n$, the edges of the subgraph $H_{i}$ we color properly with colors
\begin{center}
$\max S\left(u_{i},\alpha\right)\cdot(r+1)+1,\max
S\left(u_{i},\alpha\right)\cdot(r+1)+2,\ldots,\max
S\left(u_{i},\alpha\right)\cdot(r+1)+r$
\end{center}
\end{description}\

It is easy to see that $\gamma$ is an interval $(t\cdot
(r+1)+r)$-coloring of the graph $G\boxtimes H$. By the definition of
$\gamma$, we have $w(G\boxtimes H)\leq w(G)\cdot (r+1)+r$ and
$W(G\boxtimes H)\geq W(G)\cdot (r+1)+r$. ~$\square$
\end{proof}

The Figure \ref{example2} shows the interval $11$-coloring $\gamma$
of the graph $P_{4}\boxtimes C_{4}$ described in the proof of
Theorem \ref{mytheorem14}.\\

\begin{figure}[h]
\begin{center}
\includegraphics[height=20pc,width=25pc]{fig3.eps}\
\caption{The interval $11$-coloring $\gamma$ of the graph
$P_{4}\boxtimes C_{4}$.}\label{example2}
\end{center}
\end{figure}

Note that there are graphs $G$ and $H$ for which $G\boxtimes H\in
\mathfrak{N}$, but $G\in \mathfrak{N},H\notin\mathfrak{N}$. For
example, $K_{2}\boxtimes C_{3}\in \mathfrak{N}$, but $C_{3}\notin
\mathfrak{N}$. For regular graphs the following result was obtained
by Zhou \cite{b38}.

\begin{theorem} \label{mytheorem15} If $G$ is $1$-factorable and $H$ is a regular
graph, then $G\boxtimes H$ is also $1$-factorable.
\end{theorem}

\begin{corollary}
\label{mycorollary6} Let $G$ and $H$ be two regular graphs and $G\in
\mathfrak{N}$. Then $G\boxtimes H\in \mathfrak{N}$.
\end{corollary}

Finally, we turn our attention to interval edge colorings of the
lexicographic product of graphs. In \cite{b25} Kubale and Giaro
posed the following question:

\begin{problem}
Does $G[H]\in \mathfrak{N}$ if $G,H\in \mathfrak{N}$?
\end{problem}

We start by focusing on the special case of this problem, when $G\in
\mathfrak{N}$ and $H=nK_{1}$ for any $n\in \mathbf{N}$.

\begin{theorem}
\label{mytheorem16} If $G\in \mathfrak{N}$, then $G[nK_{1}]\in
\mathfrak{N}$ for any $n\in \mathbf{N}$. Moreover, $w(G[nK_{1}])\leq
w(G)\cdot n$ and $W(G[nK_{1}])\geq (W(G)+1)\cdot n - 1$.
\end{theorem}
\begin{proof} Let $V(G)=\{u_{1},u_{2},\ldots,u_{m}\}$ and

\begin{center}
$V\left(G[nK_{1}]\right)=\left\{v_{j}^{(i)}|~1\leq i\leq m, 1\leq
j\leq n\right\}$,
\end{center}

\begin{center}
$E\left(G[nK_{1}]\right)=\left\{\left(v_{p}^{(i)},v_{q}^{(j)}\right)|~\left(u_{i},u_{j}\right)\in
E(G)~and~p,q=1,2,\ldots,n\right\}$.
\end{center}

Let $\alpha$ be an interval $t$-coloring of the graph $G$.

Define an edge coloring $\beta$ of the graph $G[nK_{1}]$ in the
following way:

for every $\left(v_{p}^{(i)},v_{q}^{(j)}\right)\in
E\left(G[nK_{1}]\right)$

\begin{center}
$\beta\left(\left(v_{p}^{(i)},v_{q}^{(j)}\right)\right)= \left\{
\begin{tabular}{ll}
$\left(\alpha((u_{i},u_{j}))-1\right)\cdot n + p+q-1\pmod {n}$, if $p+q\neq n+1$,\\
$\alpha((u_{i},u_{j}))\cdot n$, if $p+q=n+1$.\\
\end{tabular
\right.$
\end{center}
where $1\leq i\leq m, 1\leq j\leq m, 1\leq p\leq n, 1\leq q\leq
n$.\\

It can be verified that $\beta$ is an interval $t\cdot n$-coloring
of the graph $G[nK_{1}]$. By the definition of $\beta$, we have
$w(G[nK_{1}])\leq w(G)\cdot n$.

Now we show that $W(G[nK_{1}])\geq (W(G)+1)\cdot n - 1$.

Let $\phi$ be an interval $W(G)$-coloring of the graph $G$.

Define an edge coloring $\psi$ of the graph $G[nK_{1}]$ in the
following way:

for every $\left(v_{p}^{(i)},v_{q}^{(j)}\right)\in
E\left(G[nK_{1}]\right)$

\begin{center}
$\psi\left(\left(v_{p}^{(i)},v_{q}^{(j)}\right)\right)=
\left(\phi((u_{i},u_{j}))-1\right)\cdot n + p+q-1$,
\end{center}
where $1\leq i\leq m, 1\leq j\leq m, 1\leq p\leq n, 1\leq q\leq
n$.\\

It is easy to see that $\psi$ is an interval $(W(G)\cdot
n+n-1)$-coloring of the graph $G[nK_{1}]$. ~$\square$
\end{proof}

The Figure \ref{example3} shows the interval $6$-coloring $\beta$ of
the graph $(K_{1,3}+e)[2K_{1}]$ described in the proof of Theorem
\ref{mytheorem16}.\\

\begin{figure}[h]
\begin{center}
\includegraphics[height=20pc,width=30pc]{fig4.eps}\
\caption{The interval $6$-coloring $\beta$ of the graph
$(K_{1,3}+e)[2K_{1}]$.}\label{example3}
\end{center}
\end{figure}

\begin{corollary}
\label{mycorollary7} (Kamalian, Petrosyan \cite{b22}) If $k$ is
even, then $C_{k}[nK_{1}]\in \mathfrak{N}$ and
\begin{center}
$W(C_{k}[nK_{1}])\geq 2n+\frac{n\cdot k}{2}-1$.
\end{center}
\end{corollary}

\begin{corollary}
\label{mycorollary8} (Kamalian, Petrosyan \cite{b23}) Let
$k=p2^{q}$, where $p$ is odd and $q\in \mathbf{N}$. Then
$K_{k}[nK_{1}]\in \mathfrak{N}$ and
\begin{center}
$W(K_{k}[nK_{1}])\geq (2k-p-q)\cdot n - 1$.
\end{center}
\end{corollary}

Now we show that $G[H]\in \mathfrak{N}$ if $G,H\in \mathfrak{N}$ and
$H$ is regular.

\begin{theorem}
\label{mytheorem17} If $G,H\in \mathfrak{N}$ and $H$ is an
$r$-regular graph, then $G[H]\in \mathfrak{N}$. Moreover, if $\vert
V(H)\vert= n$, then $w(G[H])\leq w(G)\cdot n + r$ and $W(G[H])\geq
W(G)\cdot n + r$.
\end{theorem}
\begin{proof} Let $V(G)=\{u_{1},u_{2},\ldots,u_{m}\}$, $V(H)=\{v_{1},v_{2},\ldots,v_{n}\}$  and

\begin{center}
$V\left(G[H]\right)=\bigcup_{i=1}^{m}V^{i}(H)$, where
$V^{i}(H)=\{w_{j}^{(i)}|~1\leq j\leq n\}$,
\end{center}

\begin{center}
$E\left(G[H]\right)=\left\{\left(w_{p}^{(i)},w_{q}^{(j)}\right)|~\left(u_{i},u_{j}\right)\in
E(G)~and~p,q=1,2,\ldots,n\right\}\cup\bigcup_{i=1}^{m}E^{i}(H)$,
where
$E^{i}(H)=\left\{\left(w_{p}^{(i)},w_{q}^{(i)}\right)|~\left(v_{p},v_{q}\right)\in
E(H)\right\}$.
\end{center}

Let $\alpha$ be an interval $t$-coloring of the graph $G$ and
\begin{center}
$H_{i}=\left(V^{i}(H),E^{i}(H)\right)$ for $i=1,2,\ldots,m$.
\end{center}

Note that $\chi ^{\prime}(H)=\Delta(H)=r$ since $H\in \mathfrak{N}$
and $H$ is an $r$-regular graph. This implies that there exists an
interval $r$-coloring of the graph $H$.

Define an edge coloring $\beta$ of the graph $G[H]$ in the following
way:

\begin{description}
\item[(1)] for every $\left(w_{p}^{(i)},w_{q}^{(j)}\right)\in E(G[H])$

\begin{center}
$\beta\left(\left(w_{p}^{(i)},w_{q}^{(j)}\right)\right)= \left\{
\begin{tabular}{ll}
$r+\left(\alpha((u_{i},u_{j}))-1\right)\cdot n + p+q-1\pmod {n}$,\\~~~~~~~~~~~~~~~~~~~~~~~~if $p+q\neq n+1$,\\
$r+\alpha((u_{i},u_{j}))\cdot n$, if $p+q=n+1$,\\
\end{tabular
\right.$
\end{center}
where $1\leq i\leq m, 1\leq j\leq m,i\neq j, 1\leq p\leq n, 1\leq
q\leq n$.\\

\item[(2)] for $i=1,2,\ldots,m$, the edges of the subgraph $H_{i}$ we color properly with colors
\begin{center}
$\left(\min S\left(u_{i},\alpha\right)-1\right)\cdot n+1,\left(\min
S\left(u_{i},\alpha\right)-1\right)\cdot n+2,\ldots,\left(\min
S\left(u_{i},\alpha\right)-1\right)\cdot n+r$
\end{center}
\end{description}\

It can be verified that $\beta$ is an interval $(t\cdot n
+r)$-coloring of the graph $G[H]$. By the definition of $\beta$, we
have $w(G[H])\leq w(G)\cdot n + r$ and $W(G[H])\geq W(G)\cdot n +
r$. ~$\square$
\end{proof}

The Figure \ref{example4} shows the interval $9$-coloring $\beta$ of
the graph $K_{4}[K_{2}]$ described in the proof of Theorem
\ref{mytheorem17}.\\

\begin{figure}[h]
\begin{center}
\includegraphics[height=20pc,width=35pc]{fig5.eps}\
\caption{The interval $9$-coloring $\beta$ of the graph
$K_{4}[K_{2}]$.}\label{example4}
\end{center}
\end{figure}

\bigskip

\section{Problems}\

We conclude with the following problems on interval edge colorings
of products of graphs.

\begin{problem}
Are there graphs $G,H\notin \mathfrak{N}$, such that $G\times H\in
\mathfrak{N}$?
\end{problem}

\begin{problem}
Are there graphs $G,H\notin \mathfrak{N}$, such that $G\otimes H\in
\mathfrak{N}$?
\end{problem}

\begin{problem}
Are there graphs $G,H\notin \mathfrak{N}$, such that $G\boxtimes
H\in \mathfrak{N}$?
\end{problem}

\bigskip

\begin{acknowledgement}
We would like to thank the anonymous referees for useful
suggestions.
\end{acknowledgement}

redpajama_set_name: RedPajamaArXiv