Excluding $K_{2,t}$ as a fat minor
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866911214600192000 |
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| author | Albrechtsen, Sandra Distel, Marc Georgakopoulos, Agelos |
| author_facet | Albrechtsen, Sandra Distel, Marc Georgakopoulos, Agelos |
| contents | We prove that for every $t \in \mathbb{N}$, the graph $K_{2,t}$ satisfies the fat minor conjecture of Georgakopoulos and Papasoglu: for every $K\in \mathbb{N}$ there exist $M,A\in \mathbb{N}$ such that every graph with no $K$-fat $K_{2,t}$ minor is $(M,A)$-quasi-isometric to a graph with no $K_{2,t}$ minor. We use this to obtain an efficient algorithm for approximating the minimal multiplicative distortion of any embedding of a finite graph into a $K_{2,t}$-minor-free graph, answering a question of Chepoi, Dragan, Newman, Rabinovich, and Vaxès from 2012. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2510_14644 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Excluding $K_{2,t}$ as a fat minor Albrechtsen, Sandra Distel, Marc Georgakopoulos, Agelos Combinatorics Computational Geometry Discrete Mathematics Metric Geometry 05C83, 05C10, 68R12, 05C63, 51F30 We prove that for every $t \in \mathbb{N}$, the graph $K_{2,t}$ satisfies the fat minor conjecture of Georgakopoulos and Papasoglu: for every $K\in \mathbb{N}$ there exist $M,A\in \mathbb{N}$ such that every graph with no $K$-fat $K_{2,t}$ minor is $(M,A)$-quasi-isometric to a graph with no $K_{2,t}$ minor. We use this to obtain an efficient algorithm for approximating the minimal multiplicative distortion of any embedding of a finite graph into a $K_{2,t}$-minor-free graph, answering a question of Chepoi, Dragan, Newman, Rabinovich, and Vaxès from 2012. |
| title | Excluding $K_{2,t}$ as a fat minor |
| topic | Combinatorics Computational Geometry Discrete Mathematics Metric Geometry 05C83, 05C10, 68R12, 05C63, 51F30 |
| url | https://arxiv.org/abs/2510.14644 |