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

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 ⌈2 3χ⌉.

• Type: Journal
• Year: 2010
• Where: JGT
• Authors: Maria Chudnovsky, Alexandra Ovetsky Fradkin
• Keywords: Chromatic Number, Claw-free Graph, JGT 2010, Pairwise Nonadjacent Neighbors