English

The chromatic gap and its extremes

Combinatorics 2020-12-01 v1

Abstract

The {\em chromatic gap} is the difference between the chromatic number and the clique number of a graph. Here we investigate \gap(n)\gap(n), the maximum chromatic gap over graphs on nn vertices. Can the extremal graphs be explored? While computational problems related to the chromatic gap are hopeless, an interplay between Ramsey theory and matching theory leads to a simple and (almost) exact formula for \gap(n)\gap(n) in terms of Ramsey numbers.

Keywords

Cite

@article{arxiv.1108.3444,
  title  = {The chromatic gap and its extremes},
  author = {András Gyárfás and András Sebõ and Nicolas Trotignon},
  journal= {arXiv preprint arXiv:1108.3444},
  year   = {2020}
}

Comments

41 pages; Cahiers Leibniz No 184, https://consult-cahiersleibniz.g-scop.grenoble-inp.fr/apps/WebObjects/CahiersLeibniz/

R2 v1 2026-06-21T18:51:36.333Z