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arXiv · 1509.06563

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

Alex Scott·Paul Seymour
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Abstract

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

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Alex Scott, Paul Seymour. 2018-02-12. Induced subgraphs of graphs with large chromatic number. IV. Consecutive holes. https://arxiv.org/abs/1509.06563

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