Obtaining trees of tangles from tangle-tree duality
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
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2020
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| _version_ | 1866918024451194880 |
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| author | Elbracht, Christian Kneip, Jay Lilian Teegen, Maximilian |
| author_facet | Elbracht, Christian Kneip, Jay Lilian Teegen, Maximilian |
| contents | We demonstrate the versatility of the tangle-tree duality theorem for abstract separation systems by using it to prove tree-of-tangles theorems. This approach allows us to strengthen some of the existing tree-of-tangles theorems by bounding the node degrees in them. We also present a slight strengthening and simplified proof of the duality theorem, which allows us to derive a tree-of-tangles theorem also for tangles of different orders. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2011_09758 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Obtaining trees of tangles from tangle-tree duality Elbracht, Christian Kneip, Jay Lilian Teegen, Maximilian Combinatorics 05C83, 05C40, 05C05 We demonstrate the versatility of the tangle-tree duality theorem for abstract separation systems by using it to prove tree-of-tangles theorems. This approach allows us to strengthen some of the existing tree-of-tangles theorems by bounding the node degrees in them. We also present a slight strengthening and simplified proof of the duality theorem, which allows us to derive a tree-of-tangles theorem also for tangles of different orders. |
| title | Obtaining trees of tangles from tangle-tree duality |
| topic | Combinatorics 05C83, 05C40, 05C05 |
| url | https://arxiv.org/abs/2011.09758 |