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

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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Publication Details

Journal
ArXiv.org
Published
2025-07-20
Primary Topic
Computational Geometry and Mesh Generation
Type
article
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article

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

Pegah Pournajafi
ArXiv.org
Computational Geometry and Mesh Generation
article

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

Pegah Pournajafi
article en

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.

ArXiv.org
Openalex Percentile: Top 42%
Computational Geometry and Mesh Generation
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A note on $χ$-unbounded classes of geometric graphs — Pegah Pournajafi · ArXiv.org (2025) | TGRS Research Map | TGRS