Graph minors and metric spaces
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866913736457977856 |
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| author | Georgakopoulos, Agelos Papasoglu, Panos |
| author_facet | Georgakopoulos, Agelos Papasoglu, Panos |
| contents | We present problems and results that combine graph-minors and coarse geometry. For example, we ask whether every geodesic metric space (or graph) without a fat $H$ minor is quasi-isometric to a graph with no $H$ minor, for an arbitrary finite graph $H$. We answer this affirmatively for a few small $H$. We also present a metric analogue of Menger's theorem and Konig's ray theorem. We conjecture metric analogues of the Erdos--Posa Theorem and Halin's grid theorem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2305_07456 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Graph minors and metric spaces Georgakopoulos, Agelos Papasoglu, Panos Combinatorics Geometric Topology Metric Geometry 51F30, 05C83, 05C10, 05C63, 20F69 We present problems and results that combine graph-minors and coarse geometry. For example, we ask whether every geodesic metric space (or graph) without a fat $H$ minor is quasi-isometric to a graph with no $H$ minor, for an arbitrary finite graph $H$. We answer this affirmatively for a few small $H$. We also present a metric analogue of Menger's theorem and Konig's ray theorem. We conjecture metric analogues of the Erdos--Posa Theorem and Halin's grid theorem. |
| title | Graph minors and metric spaces |
| topic | Combinatorics Geometric Topology Metric Geometry 51F30, 05C83, 05C10, 05C63, 20F69 |
| url | https://arxiv.org/abs/2305.07456 |