Polynomial bounds for chromatic number VIII. Excluding a path and a complete multipartite graph
Combinatorics
2023-03-22 v1
Abstract
We prove that for every path H, and every integer d, there is a polynomial f such that every graph G with chromatic number greater than f(t) either contains H as an induced subgraph, or contains as a subgraph the complete d-partite graph with parts of cardinality t. For t = 1 and general d this is a classical theorem of Gy\'arf\'as, and for d = 2 and general t this is a theorem of Bonamy et al.
Keywords
Cite
@article{arxiv.2303.11766,
title = {Polynomial bounds for chromatic number VIII. Excluding a path and a complete multipartite graph},
author = {Tung Nguyen and Alex Scott and Paul Seymour},
journal= {arXiv preprint arXiv:2303.11766},
year = {2023}
}