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arXiv · 2304.04296

A tamed family of triangle-free graphs with unbounded chromatic number

Édouard Bonnet·Romain Bourneuf·Julien Duron·Colin Geniet·Stéphan Thomassé·Nicolas Trotignon
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Abstract

We construct a hereditary class of triangle-free graphs with unbounded chromatic number, in which every non-trivial graph either contains a pair of non-adjacent twins or has an edgeless vertex cutset of size at most two. This answers in the negative a question of Chudnovsky, Penev, Scott, and Trotignon. The class is the hereditary closure of a family of (triangle-free) twincut graphs $G_1, G_2, \ldots$ such that $G_k$ has chromatic number $k$. We also show that every twincut graph is edge-critical.

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Édouard Bonnet, Romain Bourneuf, Julien Duron, Colin Geniet, Stéphan Thomassé, Nicolas Trotignon. 2023-04-09. A tamed family of triangle-free graphs with unbounded chromatic number. https://arxiv.org/abs/2304.04296

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