Trees of tangles in abstract separation systems
Christian Elbracht, Jay Lilian Kneip, Maximilian Teegen

TL;DR
This paper establishes canonical and non-canonical tree-of-tangles theorems for abstract separation systems, simplifying proofs and unifying results across graphs, matroids, and other systems with submodular order functions.
Contribution
It introduces a unified framework for tree-of-tangles theorems in abstract separation systems, extending and simplifying existing results.
Findings
Proves canonical and non-canonical tree-of-tangles theorems for submodular systems
Simplifies proofs of known theorems for graphs and matroids
Unifies various tree-of-tangles results under a common framework
Abstract
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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