English

Induced subgraphs of graphs with large chromatic number. III. Long holes

Combinatorics 2016-03-15 v2

Abstract

We prove a 1985 conjecture of Gy\'arf\'as that for all k,k,\ell, every graph with sufficiently large chromatic number contains either a complete subgraph with kk vertices or an induced cycle of length at least \ell.

Keywords

Cite

@article{arxiv.1506.02232,
  title  = {Induced subgraphs of graphs with large chromatic number. III. Long holes},
  author = {Maria Chudnovsky and Alex Scott and Paul Seymour},
  journal= {arXiv preprint arXiv:1506.02232},
  year   = {2016}
}