Strongly sublinear separators and bounded asymptotic dimension for sphere intersection graphs
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arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866908294267797504 |
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| author | Davies, James Georgakopoulos, Agelos Hatzel, Meike McCarty, Rose |
| author_facet | Davies, James Georgakopoulos, Agelos Hatzel, Meike McCarty, Rose |
| contents | In this paper, we consider the class $\mathcal{C}^d$ of sphere intersection graphs in $\mathbb{R}^d$ for $d \geq 2$. We show that for each integer $t$, the class of all graphs in $\mathcal{C}^d$ that exclude $K_{t,t}$ as a subgraph has strongly sublinear separators. We also prove that $\mathcal{C}^d$ has asymptotic dimension at most $2d+2$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_00932 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Strongly sublinear separators and bounded asymptotic dimension for sphere intersection graphs Davies, James Georgakopoulos, Agelos Hatzel, Meike McCarty, Rose Combinatorics Computational Geometry Discrete Mathematics Metric Geometry In this paper, we consider the class $\mathcal{C}^d$ of sphere intersection graphs in $\mathbb{R}^d$ for $d \geq 2$. We show that for each integer $t$, the class of all graphs in $\mathcal{C}^d$ that exclude $K_{t,t}$ as a subgraph has strongly sublinear separators. We also prove that $\mathcal{C}^d$ has asymptotic dimension at most $2d+2$. |
| title | Strongly sublinear separators and bounded asymptotic dimension for sphere intersection graphs |
| topic | Combinatorics Computational Geometry Discrete Mathematics Metric Geometry |
| url | https://arxiv.org/abs/2504.00932 |