Polynomial bounds for chromatic number. I. Excluding a biclique and an induced tree
Combinatorics
2021-07-27 v2
Abstract
Let H be a tree. It was proved by Rodl that graphs that do not contain H as an induced subgraph, and do not contain the complete bipartite graph as a subgraph, have bounded chromatic number. Kierstead and Penrice strengthened this, showing that such graphs have bounded degeneracy. Here we give a further strengthening, proving that for every tree H, the degeneracy is at most polynomial in t. This answers a question of Bonamy, Pilipczuk, Rzazewski, Thomasse and Walczak.
Keywords
Cite
@article{arxiv.2104.07927,
title = {Polynomial bounds for chromatic number. I. Excluding a biclique and an induced tree},
author = {Alex Scott and Paul Seymour and Sophie Spirkl},
journal= {arXiv preprint arXiv:2104.07927},
year = {2021}
}