A note on $χ$-unbounded classes of geometric graphs
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866909696842006528 |
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| author | Pournajafi, Pegah |
| author_facet | Pournajafi, Pegah |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_14884 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A note on $χ$-unbounded classes of geometric graphs Pournajafi, Pegah Combinatorics 05C62 (Primary) 05C15 (Secondary) 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. |
| title | A note on $χ$-unbounded classes of geometric graphs |
| topic | Combinatorics 05C62 (Primary) 05C15 (Secondary) |
| url | https://arxiv.org/abs/2507.14884 |