English

A note on acyclic vertex-colorings

Combinatorics 2013-12-20 v1

Abstract

We prove that the acyclic chromatic number of a graph with maximum degree Δ\Delta is less than 2.835Δ4/3+Δ2.835\Delta^{4/3}+\Delta. This improves the previous upper bound, which was 50Δ4/350\Delta^{4/3}. To do so, we draw inspiration from works by Alon, McDiarmid and Reed and by Esperet and Parreau.

Keywords

Cite

@article{arxiv.1312.5600,
  title  = {A note on acyclic vertex-colorings},
  author = {Jean-Sébastien Sereni and Jan Volec},
  journal= {arXiv preprint arXiv:1312.5600},
  year   = {2013}
}
R2 v1 2026-06-22T02:31:42.984Z