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List-Coloring Claw-Free Graphs with Small Clique Number

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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.

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Authors and Affiliations

  1. CNRS/Grenoble-INP/UJF-Grenoble 1, G-SCOP (UMR5272), Grenoble, France

    Louis Esperet & Frédéric Maffray

  2. Rényi Institute, Budapest, Hungary

    András Gyárfás

Authors
  1. Louis Esperet
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  2. András Gyárfás
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  3. Frédéric Maffray
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Corresponding author

Correspondence to Louis Esperet.

Additional information

Research supported in part by ANR Project Heredia under Contract anr- 10- jcjc- 0204- 01.

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Esperet, L., Gyárfás, A. & Maffray, F. List-Coloring Claw-Free Graphs with Small Clique Number. Graphs and Combinatorics 30, 365–375 (2014). https://doi.org/10.1007/s00373-012-1272-x

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  • DOI: https://doi.org/10.1007/s00373-012-1272-x

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