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Coloring Dense Digraphs

Abstract : The chromatic number of a digraph D is the minimum number of acyclic subgraphs covering the vertex set of D. A tournament H is a hero if every H-free tournament T has chromatic number bounded by a function of H. Inspired by the celebrated Erdős-Hajnal conjecture, Berger et al. fully characterized the class of heroes in 2013. We extend this framework to dense digraphs: A digraph H is a superhero if every H-free digraph D has chromatic number bounded by a function of H and α(D), the independence number of the underlying graph of D. We prove here that a digraph is a superhero if and only if it is a hero, and hence characterize all superheroes. This answers a question of Aboulker, Charbit and Naserasr.
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https://hal.archives-ouvertes.fr/hal-02935899
Contributor : Stéphan Thomassé <>
Submitted on : Thursday, September 10, 2020 - 5:21:40 PM
Last modification on : Saturday, September 11, 2021 - 3:19:38 AM

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Ararat Harutyunyan, Tien-Nam Le, Alantha Newman, Stéphan Thomassé. Coloring Dense Digraphs. Combinatorica, Springer Verlag, 2019, 39 (5), pp.1021-1053. ⟨10.1007/s00493-019-3815-8⟩. ⟨hal-02935899⟩

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