A note on acyclic vertex-colorings

Abstract

We prove that the acyclic chromatic number of a graph with maximum degree $\Delta$ is less than $2.835{\Delta }^{4/3}+\Delta$. This improves the previous upper bound, which was $50{\Delta }^{4/3}$. To do so, we draw inspiration from works by Alon, McDiarmid and Reed and by Esperet and Parreau.

References in corpus (1)

• Acyclic edge-coloring using entropy compression

Cited by in corpus (1)

• The Thue choice number versus the Thue chromatic number of graphs