A stronger bound for the strong chromatic index

Henning Bruhn; Felix Joos

A stronger bound for the strong chromatic index

Combinatorics 2015-04-13 v1 Discrete Mathematics Probability

Authors: Henning Bruhn , Felix Joos

Abstract

We prove $\chi_s'(G)\leq 1.93 \Delta(G)^2$ for graphs of sufficiently large maximum degree where $\chi_s'(G)$ is the strong chromatic index of $G$ . This improves an old bound of Molloy and Reed. As a by-product, we present a Talagrand-type inequality where it is allowed to exclude unlikely bad outcomes that would otherwise render the inequality unusable.

Keywords

graph coloring

Cite

@article{arxiv.1504.02583,
  title  = {A stronger bound for the strong chromatic index},
  author = {Henning Bruhn and Felix Joos},
  journal= {arXiv preprint arXiv:1504.02583},
  year   = {2015}
}

Comments

22 pages

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