An approximate version of Hadwiger's conjecture for claw-free graphs

Authors


  • Part of this research was conducted while Maria Chudnovsky served as a Clay Mathematics Institute Research Fellow.

Abstract

Hadwiger's conjecture states that every graph with chromatic number χ has a clique minor of size χ. In this paper we prove a weakened version of this conjecture for the class of claw-free graphs (graphs that do not have a vertex with three pairwise nonadjacent neighbors). Our main result is that a claw-free graph with chromatic number χ has a clique minor of size equation image. © 2009 Wiley Periodicals, Inc. J Graph Theory 63: 259–278, 2010

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