Journal
JOURNAL OF COMBINATORIAL THEORY SERIES B
Volume 100, Issue 6, Pages 560-572Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jctb.2010.04.005
Keywords
Claw-free graphs; Colouring; Choosability
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Funding
- NSF [DMS-0758364, DMS03-54465]
- ONR [N00014-04-1-0062]
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In this paper we prove that if G is a connected claw-free graph with three pairwise non-adjacent vertices, with chromatic number x and clique number omega, then x <= 2 omega and the same for the complement of G. We also prove that the choice number of G is at most 2 omega. except possibly in the case when G can be obtained from a subgraph of the Schlafli graph by replicating vertices. Finally, we show that the constant 2 is best possible in all cases. (C) 2010 Elsevier Inc. All rights reserved.
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