English

Equitable Colorings of $K\_4$-minor-free Graphs

Combinatorics 2017-03-08 v1

Abstract

We demonstrate that for every positive integer Δ\Delta, every K\_4-minor-free graph with maximum degree Δ\Delta admits an equitable coloring with k colors wherek \ge (Δ\Delta+3)/2. This bound is tight and confirms a conjecture by Zhang and Whu. We do not use the discharging method but rather exploit decomposition trees of K 4-minor-free graphs.

Keywords

Cite

@article{arxiv.1703.02250,
  title  = {Equitable Colorings of $K\_4$-minor-free Graphs},
  author = {Rémi De Joannis de Verclos and Jean-Sébastien Sereni},
  journal= {arXiv preprint arXiv:1703.02250},
  year   = {2017}
}