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Journal Articles Journal of Graph Theory Year : 2018

Subdivisions of oriented cycles in digraphs with large chromatic number

Abstract

An oriented cycle is an orientation of a undirected cycle. We first show that for any oriented cycle C, there are digraphs containing no subdivision of C (as a subdigraph) and arbitrarily large chromatic number. In contrast, we show that for any C a cycle with two blocks, every strongly connected digraph with sufficiently large chromatic number contains a subdivision of C. We prove a similar result for the antidirected cycle on four vertices (in which two vertices have out-degree 2 and two vertices have in-degree 2).
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Dates and versions

hal-01834779 , version 1 (10-07-2018)

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Nathann Cohen, Frédéric Havet, William Lochet, Nicolas Nisse. Subdivisions of oriented cycles in digraphs with large chromatic number. Journal of Graph Theory, 2018, 89 (4), pp.439-456. ⟨10.1002/jgt.22360⟩. ⟨hal-01834779⟩
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