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arXiv · 2611.06699

Polylogarithmic bound for the Gyárfás-Sumner conjecture

Martin Bierbaumer·Matija Bucić
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Abstract

The classical Gyárfás-Sumner conjecture asserts that for any fixed forest $F$, any graph $G$ not containing $F$ as an induced subgraph, with bounded clique number $ω(G)$, has bounded chromatic number $χ(G)$. Recently, Nguyen, Scott, and Seymour proved that every such graph has chromatic number at most $|G|^{o(1)}$. We improve this bound to a polylogarithmic one $(\log |G|)^{O(1)}$.

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Martin Bierbaumer, Matija Bucić. 2026-11-04. Polylogarithmic bound for the Gyárfás-Sumner conjecture. https://arxiv.org/abs/2611.06699

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