Displaying tangles and non-sequential separations

Abstract

We show that, for any graph or matroid, there is a tree that simultaneously distinguishes its maximal tangles, and, for each maximal tangle $\mathcal{T}$ that satisfies an additional robustness condition, displays all of the non-trivial separations relative to $\mathcal{T}$, up to a natural equivalence.

9 pages. arXiv admin note: text overlap with arXiv:1109.1048