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Pré-Publication, Document De Travail Année : 2017

Graphs with large chromatic number induce 3k-cycles

Résumé

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.

Dates et versions

hal-01431393 , version 1 (10-01-2017)

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Marthe Bonamy, Stéphan Thomassé, Pierre Charbit. Graphs with large chromatic number induce 3k-cycles. 2017. ⟨hal-01431393⟩
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