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arXiv · 1706.00337

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

Zdeněk Dvořák·Ken-ichi Kawarabayashi
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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.

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Zdeněk Dvořák, Ken-ichi Kawarabayashi. 2017-06-09. Triangle-free graphs of tree-width t are ceil((t + 3)/2)-colorable. https://arxiv.org/abs/1706.00337

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