A note on $χ$-unbounded classes of geometric graphs

Pegah Pournajafi

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arXiv · 2507.14884

A note on $χ$-unbounded classes of geometric graphs

Pegah Pournajafi

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Abstract

We show that there exist infinitely many classes of intersection graphs of geometric objects that are not $χ$-bounded -- namely, $d$-CBU graphs for $d\geq 3$ -- and each is incomparable with the class of Burling graphs. This answers a folklore open problem on whether Burling graphs are the sole source of unbounded chromatic number among geometric intersection classes.

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Pegah Pournajafi. 2025-07-20. A note on $χ$-unbounded classes of geometric graphs. https://arxiv.org/abs/2507.14884

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