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 , there is a function such that if does not contain as an induced subgraph then (where are the chromatic number and the clique number of ). Here we prove that can be chosen to be a polynomial.
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}
}