A note on acyclic vertex-colorings

Jean-Sébastien Sereni 1 Jan Volec 2
1 ORPAILLEUR - Knowledge representation, reasonning
Inria Nancy - Grand Est, LORIA - NLPKD - Department of Natural Language Processing & Knowledge Discovery
Abstract : We prove that the acyclic chromatic number of a graph with maximum degree ∆ is less than 2.835∆4/3+∆. This improves the previous upper bound, which was 50∆4/3. To do so, we draw inspiration from works by Alon, McDiarmid and Reed and by Esperet and Parreau.
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Jean-Sébastien Sereni, Jan Volec. A note on acyclic vertex-colorings. Journal of Combinatorics, International Press, 2016, 7 (4), pp.725--737. ⟨10.4310/JOC.2016.v7.n4.a8⟩. ⟨hal-00921122⟩

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