Clique minors in claw-free graphs

Authors:
Alexandra Fradkin
Affiliations:
Princeton University, Princeton, NJ 08544, USA
Venue:
Journal of Combinatorial Theory Series B
Year:
2012

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Abstract

Hadwiger@?s conjecture states that every graph with chromatic number @g has a clique minor of size @g. Let G be a graph on n vertices with chromatic number @g and stability number @a. Then since @g@a=n, Hadwiger@?s conjecture implies that G has a clique minor of size n@a. In this paper we prove that this is true for connected claw-free graphs with @a=3. We also show that this result is tight by providing an infinite family of claw-free graphs with @a=3 that do not have a clique minor of size larger than n@a.