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

نویسندگان

Maria Chudnovsky

Alexandra Ovetsky Fradkin

چکیده

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 ⌈23χ⌉.

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