English

Arboricity and Acyclic Chromatic Number

Combinatorics 2023-11-07 v1 Discrete Mathematics

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 Gr\"unbaum conjecture from 1973.

Keywords

Cite

@article{arxiv.2311.03049,
  title  = {Arboricity and Acyclic Chromatic Number},
  author = {Oliver Knill},
  journal= {arXiv preprint arXiv:2311.03049},
  year   = {2023}
}

Comments

4 pages

R2 v1 2026-06-28T13:12:35.818Z