Fat minors cannot be thinned (by quasi-isometries)
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866911877254086656 |
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| author | Davies, James Hickingbotham, Robert Illingworth, Freddie McCarty, Rose |
| author_facet | Davies, James Hickingbotham, Robert Illingworth, Freddie McCarty, Rose |
| contents | We disprove the conjecture of Georgakopoulos and Papasoglu that a length space (or graph) with no $K$-fat $H$ minor is quasi-isometric to a graph with no $H$ minor. Our counterexample is furthermore not quasi-isometric to a graph with no 2-fat $H$ minor or a length space with no $H$ minor. On the other hand, we show that the following weakening holds: any graph with no $K$-fat $H$ minor is quasi-isometric to a graph with no $3$-fat $H$ minor. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_09383 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Fat minors cannot be thinned (by quasi-isometries) Davies, James Hickingbotham, Robert Illingworth, Freddie McCarty, Rose Combinatorics Metric Geometry We disprove the conjecture of Georgakopoulos and Papasoglu that a length space (or graph) with no $K$-fat $H$ minor is quasi-isometric to a graph with no $H$ minor. Our counterexample is furthermore not quasi-isometric to a graph with no 2-fat $H$ minor or a length space with no $H$ minor. On the other hand, we show that the following weakening holds: any graph with no $K$-fat $H$ minor is quasi-isometric to a graph with no $3$-fat $H$ minor. |
| title | Fat minors cannot be thinned (by quasi-isometries) |
| topic | Combinatorics Metric Geometry |
| url | https://arxiv.org/abs/2405.09383 |