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arXiv · 2311.03049

Arboricity and Acyclic Chromatic Number

Oliver Knill
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Abstract

A theorem of Hakimi, Mitchem and Schmeichel from 1996 states that the edge arboricity arb(G) of a graph is bounded above by the acyclic chromatic number acy(G). We can improve this HMS inequality by 1, if acy(G) is even. We review also results about acyclic chromatic numbers in the context of a Grünbaum conjecture from 1973.

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Oliver Knill. 2023-11-06. Arboricity and Acyclic Chromatic Number. https://arxiv.org/abs/2311.03049

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