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Journal Articles Discrete Mathematics Year : 2020

Acyclic coloring of graphs and entropy compression method

Abstract

Based on the algorithmic proof of Lovász local lemma due to Moser and Tardos, Dujmović et al. (2016) initiated the use of the so-called entropy compression method for graph coloring problems. Then, using the same approach Esperet and Parreau (2013) proved new upper bounds for several chromatic numbers, and explained how that approach could be used for many different coloring problems. Here, we follow this line of research for the particular case of acyclic coloring: we show that every graph with maximum degree \Delta has acyclic chromatic number at most \frac{3}{2}\Delta^\frac{4}{3}+0(\Delta).
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Dates and versions

lirmm-02938618 , version 1 (15-12-2020)

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Daniel Gonçalves, Mickaël Montassier, Alexandre Pinlou. Acyclic coloring of graphs and entropy compression method. Discrete Mathematics, 2020, 343 (4), pp.#111772. ⟨10.1016/j.disc.2019.111772⟩. ⟨lirmm-02938618⟩
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