Polynomial bounds for chromatic number. III. Excluding a double star
Abstract
A double star is a tree with two internal vertices. It is known that the Gy\'arf\'as-Sumner conjecture holds for double stars, that is, for every double star H, there is a function f such that if G does not contain H as an induced subgraph then (G) f(ω(G)) (where , ω are the chromatic number and the clique number of G). Here we prove that f can be chosen to be a polynomial.
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