Are all forms of Dukkha related to a sense of self? A few days ago I started reading books about Paticcasamuppada because I realized how little and shallow was my understanding on this capital matter.

Despite getting the gist of it, I still have problems understanding the exact details.

For instance, I understand that dukkha arises from the 3 kinds of craving (kama, bhava, vibhava), and that craving is the condition for the arising of sustenance/clinging/fuel.

I've been reading a book based on Dhamma Talks given by Buddhadasa Bhikkhu (Under the Bodhi Tree) on the topic of Dependent Co-arising. There it is said that all kinds of suffering are born from clinging to "I" and "mine".  Is that always the case?

If attachment and obsession is developed towards some kind of feeling, is always the idea of a self involved in that process? Couldn't be the case of some obsession to, for example, a pleasent feeling without thinking about it as "mine" or "me"? Couldn't we just attached to a past feeling on itself?

Or to put it in other words...

Is the arising of the idea/perception of self always necessary for the arising of dukkha?

I'm not sure if I'm expressing my doubts correctly. 

Thanks in advance for your time and patience.
From the second noble truth, we know that suffering (dukkha) is caused by craving (tanha). From the third noble truth, we know that the cessation of suffering comes through the cessation of craving.

What is craving really?

From this answer, we learn that craving is a habit of reification or objectification-classification (papañca). I quote that answer here:


  Reification is simpistic naive superficial perception. It's a
  generalization of the same problem that children have with toys. A
  child sees a new shiny toy and because he does not think deeply,
  because his perception is superficial - in his mind the toy is
  attractive and desirable.
  
  Reification is seeing the outer image and buying into its glow, its
  fake promise to make you happy.


Meanwhile, in this question, I quoted Sutta Nipata 4.14:


  Seeing in what way is a monk unbound, clinging to nothing in the
  world?"
  "He should put an entire stop to the root of
  objectification-classifications (papañca): 'I am the thinker.'
  
  Commentary (Thanissaro):
  The perception, "I am the thinker" lies at the root of these classifications in that it reads into the
  immediate present a set of distinctions — I/not-I; being/not-being;
  thinker/thought; identity/non-identity — that then can proliferate
  into mental and physical conflict. The conceit inherent in this
  perception thus forms a fetter on the mind. To become unbound, one
  must learn to examine these distinctions — which we all take for
  granted — to see that they are simply assumptions that are not
  inherent in experience, and that we would be better off to be able to
  drop them.


Now what is the notion of the self? It's a mental fabrication. It's a view. It's a thought in the mind.

Due to this deep-seated thought or view of "I am the thinker" i.e. the notion of the self, one reifies everything that is perceived through the six senses into objects and classifies them according to its relationship to the self. It creates the duality of self and non-self, as well as classifies the relationship of non-self things to the self e.g. this belongs to me, that does not belong to me. Without the notion of the self, this reification would not exist.

And craving is, as said above, just a habit of reification.

For e.g. when you look at food that looks interesting to you, you experience craving. When the food is not present and you think about it, that's clinging. When you try to get this food, but it is denied to you, you experience anger. If somebody else took the last piece of that food and it is denied to you, you feel jealous as you see them relishing it.

To you, that meat thing on the plate looks like delicious food. To a vegan, that may look repulsive.

Why is this the case? That thing on the plate is just a thing. It's your mind that objectified it and classified it as delicious food. The vegan's mind objectified it and classified it as repulsive food.

Isn't it delicious food, only relative to you (the self) and your eating preferences (some characteristic of your personality i.e. part of your self)?

To a honey bee, that meat thing on the plate is not even food, because that's not the kind of food that it eats. That's just dirt to the bee. The bee objectifies it and classifies it relative to its self.

So, all types of craving and clinging and views are all relative to your self. If there is no notion of self, then the (sight and smell of the) thing on the plate is just something on the plate, that evokes no emotion.

So, all forms of sufferings are indeed related to the notion of the self.