Optimal trees of tangles: refining the essential parts
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866910191041118208 |
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| author | Albrechtsen, Sandra |
| author_facet | Albrechtsen, Sandra |
| contents | We combine the two fundamental fixed-order tangle theorems of Robertson and Seymour into a single theorem that implies both, in a best possible way.
We show that, for every $k \in \mathbb{N}$, every tree-decomposition of a graph $G$ which efficiently distinguishes all its $k$-tangles can be refined to a tree-decomposition whose parts are either too small to be home to a $k$-tangle, or as small as possible while being home to a $k$-tangle. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2304_12078 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Optimal trees of tangles: refining the essential parts Albrechtsen, Sandra Combinatorics 05C83 (Primary), 05C40, 06A07 (Secondary) We combine the two fundamental fixed-order tangle theorems of Robertson and Seymour into a single theorem that implies both, in a best possible way. We show that, for every $k \in \mathbb{N}$, every tree-decomposition of a graph $G$ which efficiently distinguishes all its $k$-tangles can be refined to a tree-decomposition whose parts are either too small to be home to a $k$-tangle, or as small as possible while being home to a $k$-tangle. |
| title | Optimal trees of tangles: refining the essential parts |
| topic | Combinatorics 05C83 (Primary), 05C40, 06A07 (Secondary) |
| url | https://arxiv.org/abs/2304.12078 |