What is an example of a biodegradable polyethylene?
In a short research I found little to no evidence, that a there is  polypropylene/polyethylene, that can actually be called biodegradeable. I have found a couple of articles that have this as a topic. I don't have the time to actually read all of them and since this is going to be to long for a comment, I'll share it as an answer.


S. Bonhomme, A. Cuer, A-M. Delort, J. Lemaire, M. Sancelme, G. Scott, Polymer Degradation and Stability 2003, 81, 441–452.
This is a general overview of the mechanisms of biodegradation of such materials.
Ignacy Jakubowicz, Polymer Degradation and Stability 2003, 80, 39–43.
This article investigates the degradation of polymers, which contain pro-oxidant additives. It mainly focusses on the kinetics of the thermo-oxidative degradation. I am certain you can learn from this article which kind of additives are used to make braking long polymers into oligomers easier and hence complete degradation faster.
Prasun K. Roy, Minna Hakkarainen, Indra K. Varma, Ann-Christine Albertsson, Environ. Sci. Technol. 2011, 45 (10), 4217–4227.
This article is very promising as it also deals with some long-term effects of polymers with pro-oxidative additives. The abstract already lays out the main problem, when talking about biodegradation: entering the eco-cycle harmlessly.


  However, the “degradable polyethylene” which is presently being promoted as an environmentally friendly alternative to the nondegradable counterpart, does not seem to meet this criterion. [...] It appears from the existing literature that our search for biodegradable polyethylene has not yet been realized.
  (Emphasis by me.)



All in all I think it is very important to carefully outline, what biodegradation is or should be. I hope these few articles can be a starting point for your further research.