English

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

Combinatorics 2021-08-17 v1

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 HH, there is a function ff such that if GG does not contain HH as an induced subgraph then χ(G)f(ω(G))\chi(G)\le f(\omega(G)) (where χ,ω\chi, \omega are the chromatic number and the clique number of GG). Here we prove that ff can be chosen to be a polynomial.

Keywords

Cite

@article{arxiv.2108.07066,
  title  = {Polynomial bounds for chromatic number. III. Excluding a double star},
  author = {Alex Scott and Paul Seymour and Sophie Spirkl},
  journal= {arXiv preprint arXiv:2108.07066},
  year   = {2021}
}
R2 v1 2026-06-24T05:09:00.645Z