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Trees of tangles in abstract separation systems

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arxiv 1909.09030 v2 pith:JKABQ2HP submitted 2019-09-19 math.CO

Christian Elbracht , Jay Lilian Kneip , Maximilian Teegen This is my paper · ORCID
classification math.CO
keywords abstractseparationsystemssubmodulartheoremstree-of-tanglescanonicalfunctions
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We prove canonical and non-canonical tree-of-tangles theorems for abstract separation systems that are merely structurally submodular. Our results imply all known tree-of-tangles theorems for graphs, matroids and abstract separation systems with submodular order functions, with greatly simplified and shortened proofs.

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  1. On vertex sets inducing tangles

    math.CO 2024-11 conditional novelty 7.0 of 10

    Every k-tangle in a graph is the lift of a k-tangle in a topological minor of size bounded by a function of k, reducing the vertex-set induction problem to bounded-size graphs.

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