Claw-free graphs VI. Colouring

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Abstract

In this paper we prove that if G is a connected claw-free graph with three pairwise non-adjacent vertices, with chromatic number χ and clique number ω, then χ≤2ω and the same for the complement of G. We also prove that the choice number of G is at most 2. ω, except possibly in the case when G can be obtained from a subgraph of the Schläfli graph by replicating vertices. Finally, we show that the constant 2 is best possible in all cases.

Original languageEnglish (US)
Pages (from-to)560-572
Number of pages13
JournalJournal of Combinatorial Theory. Series B
Volume100
Issue number6
DOIs
StatePublished - Nov 1 2010

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics
  • Computational Theory and Mathematics

Keywords

  • Choosability
  • Claw-free graphs
  • Colouring

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