English

A survey of $\chi$-boundedness

Combinatorics 2020-05-26 v3

Abstract

If a graph has bounded clique number, and sufficiently large chromatic number, what can we say about its induced subgraphs? Andr\'as Gy\'arf\'as made a number of challenging conjectures about this in the early 1980's, which have remained open until recently; but in the last few years there has been substantial progress. This is a survey of where we are now.

Keywords

Cite

@article{arxiv.1812.07500,
  title  = {A survey of $\chi$-boundedness},
  author = {Alex Scott and Paul Seymour},
  journal= {arXiv preprint arXiv:1812.07500},
  year   = {2020}
}
R2 v1 2026-06-23T06:46:38.033Z