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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2408.15335 |
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| _version_ | 1866914162174590976 |
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| author | Albrechtsen, Sandra Jacobs, Raphael W. Knappe, Paul Wollan, Paul |
| author_facet | Albrechtsen, Sandra Jacobs, Raphael W. Knappe, Paul Wollan, Paul |
| contents | We prove that there is a function $f$ such that every graph with no $K$-fat $K_4$ minor is $f(K)$-quasi-isometric to a graph with no $K_4$ minor. This solves the $K_4$-case of a general conjecture of Georgakopoulos and Papasoglu. Our proof technique also yields a new short proof of the respective $K_4^-$-case, which was first established by Fujiwara and Papasoglu. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_15335 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A characterisation of graphs quasi-isometric to $K_4$-minor-free graphs Albrechtsen, Sandra Jacobs, Raphael W. Knappe, Paul Wollan, Paul Combinatorics Metric Geometry 51F30, 05C83, 05C10 We prove that there is a function $f$ such that every graph with no $K$-fat $K_4$ minor is $f(K)$-quasi-isometric to a graph with no $K_4$ minor. This solves the $K_4$-case of a general conjecture of Georgakopoulos and Papasoglu. Our proof technique also yields a new short proof of the respective $K_4^-$-case, which was first established by Fujiwara and Papasoglu. |
| title | A characterisation of graphs quasi-isometric to $K_4$-minor-free graphs |
| topic | Combinatorics Metric Geometry 51F30, 05C83, 05C10 |
| url | https://arxiv.org/abs/2408.15335 |