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arXiv · 1408.2172

Graphs with large chromatic number induce $3k$-cycles

Marthe Bonamy·Pierre Charbit·Stéphan Thomassé
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Abstract

Answering a question of Kalai and Meshulam, we prove that graphs without induced cycles of length $3k$ have bounded chromatic number. This implies the very first case of a much broader question asserting that every graph with large chromatic number induces a graph $H$ such that the sum of the Betti numbers of the independence complex of $H$ is also large.

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Marthe Bonamy, Pierre Charbit, Stéphan Thomassé. 2014-08-10. Graphs with large chromatic number induce $3k$-cycles. https://arxiv.org/abs/1408.2172

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