Ends as tangles
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2019
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| _version_ | 1866912376964513792 |
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| author | Kneip, Jay Lilian |
| author_facet | Kneip, Jay Lilian |
| contents | Every end of an infinite graph $ G $ defines a tangle of infinite order in $ G $. These tangles indicate a highly cohesive substructure in the graph if and only if they are closed in some natural topology. We characterize, for every finite $ k $, the ends $ ω$ whose induced tangles of order $ k $ are closed. They are precisely the tangles $ τ$ for which there is a set of $ k $ vertices that decides $ τ$ by majority vote. Such a set exists if and only if the vertex degree plus the number of dominating vertices of $ ω$ is at least $ k $. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1909_12628 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | Ends as tangles Kneip, Jay Lilian Combinatorics Every end of an infinite graph $ G $ defines a tangle of infinite order in $ G $. These tangles indicate a highly cohesive substructure in the graph if and only if they are closed in some natural topology. We characterize, for every finite $ k $, the ends $ ω$ whose induced tangles of order $ k $ are closed. They are precisely the tangles $ τ$ for which there is a set of $ k $ vertices that decides $ τ$ by majority vote. Such a set exists if and only if the vertex degree plus the number of dominating vertices of $ ω$ is at least $ k $. |
| title | Ends as tangles |
| topic | Combinatorics |
| url | https://arxiv.org/abs/1909.12628 |