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