A note on acyclic vertex-colorings

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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