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Graphs with large chromatic number induce 3k-cycles

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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Preprints, Working Papers, ...
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Contributor : Marthe Bonamy <>
Submitted on : Tuesday, January 10, 2017 - 5:23:10 PM
Last modification on : Saturday, September 11, 2021 - 3:18:32 AM

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  • HAL Id : hal-01431393, version 1
  • ARXIV : 1408.2172


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



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