On the choosability of claw-free perfect graphs
Combinatorics
2015-11-24 v3
Abstract
It has been conjectured that for every claw-free graph the choice number of is equal to its chromatic number. We focus on the special case of this conjecture where 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 .
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}
}