Obtaining trees of tangles from tangle-tree duality

We demonstrate the versatility of the tangle-tree duality theorem for abstract separation systems [7] 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.

Keywords

tangles, tree-decompositions, abstract separation systems, tangle-tree duality, tree of tangles

2010 Mathematics Subject Classification

05C05, 05C40, 05C83

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Received 23 February 2021

Accepted 27 February 2021

Published 30 March 2022