Induced subgraphs of graphs with large chromatic number. I. Odd holes
Combinatorics
2015-09-01 v3
Abstract
An odd hole in a graph is an induced subgraph which is a cycle of odd length at least five. In 1985, A. Gyarfas made the conjecture that for all t there exists n such that every graph with no K_t subgraph and no odd hole is n-colourable. We prove this conjecture.
Cite
@article{arxiv.1410.4118,
title = {Induced subgraphs of graphs with large chromatic number. I. Odd holes},
author = {Alex Scott and Paul Seymour},
journal= {arXiv preprint arXiv:1410.4118},
year = {2015}
}