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arXiv · 1312.5600

A note on acyclic vertex-colorings

Jean-Sébastien Sereni·Jan Volec
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Abstract

We prove that the acyclic chromatic number of a graph with maximum degree $Δ$ is less than $2.835Δ^{4/3}+Δ$. This improves the previous upper bound, which was $50Δ^{4/3}$. 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. 2013-12-19. A note on acyclic vertex-colorings. https://arxiv.org/abs/1312.5600

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