Graph Skeletons and Diminishing Minors
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866912080900128768 |
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| author | Bruner, Michael Mitra, Atish Steiger, Heidi |
| author_facet | Bruner, Michael Mitra, Atish Steiger, Heidi |
| contents | We introduce the notion of coarse bottlenecking in graphs and coarse skeletons of graphs and show how bottlenecking guarantees that a skeleton resembles (up to quasi-isometry) the original graph. We show how these tools can be used to simplify the structure of graphs upto quasi-isometry that have an excluded asymptotic minor, reducing it to a skeleton of the original containing no $3$-fat minor. We give an example to show that a similar result does not hold for $2$-fat minors. This makes progress towards a Conjecture posed by Georgakopoulos and Papasoglu. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_17785 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Graph Skeletons and Diminishing Minors Bruner, Michael Mitra, Atish Steiger, Heidi Metric Geometry Combinatorics 51F30, 05C10 We introduce the notion of coarse bottlenecking in graphs and coarse skeletons of graphs and show how bottlenecking guarantees that a skeleton resembles (up to quasi-isometry) the original graph. We show how these tools can be used to simplify the structure of graphs upto quasi-isometry that have an excluded asymptotic minor, reducing it to a skeleton of the original containing no $3$-fat minor. We give an example to show that a similar result does not hold for $2$-fat minors. This makes progress towards a Conjecture posed by Georgakopoulos and Papasoglu. |
| title | Graph Skeletons and Diminishing Minors |
| topic | Metric Geometry Combinatorics 51F30, 05C10 |
| url | https://arxiv.org/abs/2405.17785 |