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arXiv · 2108.07066

Polynomial bounds for chromatic number. III. Excluding a double star

Alex Scott·Paul Seymour·Sophie Spirkl
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Abstract

A double star is a tree with two internal vertices. It is known that the Gyárfás-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 $χ(G)\le f(ω(G))$ (where $χ, ω$ 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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Alex Scott, Paul Seymour, Sophie Spirkl. 2021-08-16. Polynomial bounds for chromatic number. III. Excluding a double star. https://arxiv.org/abs/2108.07066

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