Can I install a back bike rack without attachment to the rear part of the frame? Can I install a back bike rack without attachment to the rear part of the frame?

Also, if someone can clarify, whenever I google 


  bike rack


I get hits on racks designed to carry bikes on a car and such.

I am referring to the racks on the bikes themselves which will allow me to haul things on my bike.

I bought a bike recently assuming it would have attachments near the rear part of the frame but they are not present. 

I have seen some bike racks which secure only to the rear wheel axle, but that does not seem too stable.

As you can see in the pic there are no holes for screwing into like I see in many other bikes and nearly all of the racks I looked at.
Several manufacturers make replacement seatpost collars with integrated rack mount holes. Just make sure you get the right diameter for your seat tube. Here is an example: