Induced subgraphs of graphs with large chromatic number. IV. Consecutive holes

Abstract

A hole in a graph is an induced subgraph which is a cycle of length at least four. We prove that for all ν > 0, every triangle-free graph with sufficiently large chromatic number contains holes of ν consecutive lengths. 

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Cite this paper

@inproceedings{Scott2015InducedSO, title={Induced subgraphs of graphs with large chromatic number. IV. Consecutive holes}, author={Alex D. Scott and Paul D. Seymour}, year={2015} }