English

A note on $\chi$-unbounded classes of geometric graphs

Combinatorics 2025-07-22 v1

Abstract

We show that there exist infinitely many classes of intersection graphs of geometric objects that are not χ\chi-bounded -- namely, dd-CBU graphs for d3d\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.

Keywords

Cite

@article{arxiv.2507.14884,
  title  = {A note on $\chi$-unbounded classes of geometric graphs},
  author = {Pegah Pournajafi},
  journal= {arXiv preprint arXiv:2507.14884},
  year   = {2025}
}

Comments

2 pages, 1 figure

R2 v1 2026-07-01T04:09:48.796Z