English

On the choosability of claw-free perfect graphs

Combinatorics 2015-11-24 v3

Abstract

It has been conjectured that for every claw-free graph GG the choice number of GG is equal to its chromatic number. We focus on the special case of this conjecture where GG is perfect. Claw-free perfect graphs can be decomposed via clique-cutset into two special classes called elementary graphs and peculiar graphs. Based on this decomposition we prove that the conjecture holds true for every claw-free perfect graph with maximum clique size at most 44.

Keywords

Cite

@article{arxiv.1506.02576,
  title  = {On the choosability of claw-free perfect graphs},
  author = {Sylvain Gravier and Frédéric Maffray and Lucas Pastor},
  journal= {arXiv preprint arXiv:1506.02576},
  year   = {2015}
}