English

Triangle-free graphs of tree-width t are ceil((t + 3)/2)-colorable

Combinatorics 2017-06-12 v2

Abstract

We prove that every triangle-free graph of tree-width t has chromatic number at most ceil((t + 3)/2), and demonstrate that this bound is tight. The argument also establishes a connection between coloring graphs of tree-width t and on-line coloring of graphs of path-width t.

Keywords

Cite

@article{arxiv.1706.00337,
  title  = {Triangle-free graphs of tree-width t are ceil((t + 3)/2)-colorable},
  author = {Zdeněk Dvořák and Ken-ichi Kawarabayashi},
  journal= {arXiv preprint arXiv:1706.00337},
  year   = {2017}
}

Comments

10 pages, no figures; updated according to referee suggestions