List-Coloring Claw-Free Graphs with Small Clique Number

Abstract

Chudnovsky and Seymour proved that every connected claw-free graph that contains a stable set of size 3 has chromatic number at most twice its clique number. We improve this for small clique size, showing that every claw-free graph with clique number at most 3 is 4-choosable and every claw-free graph with clique number at most 4 is 7-choosable. These bounds are tight.

DOI: 10.1007/s00373-012-1272-x

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Cite this paper

@article{Esperet2014ListColoringCG, title={List-Coloring Claw-Free Graphs with Small Clique Number}, author={Louis Esperet and Andr{\'a}s Gy{\'a}rf{\'a}s and Fr{\'e}d{\'e}ric Maffray}, journal={Graphs and Combinatorics}, year={2014}, volume={30}, pages={365-375} }