Tangles, as introduced by Robertson and Seymour, were designed as an indirect way of capturing clusters in graphs and matroids. They have since been shown to capture clusters in much broader discrete structures too. But not all tangles are induced by a cluster. We characterise those that are: the tangles that have a decider. We offer two such characterisations. The first is in terms of how many small sides of a tangle's separations it takes to cover the graph or matroid. The second uses a new notion of duality for sets of separations that do not necessarily come from graphs or matroids.Comment: 18 page
AbstractA tangle in a matroid is an obstruction to small branch-width. In particular, the maximum or...
Let M be a 3-connected matroid, and let N be a 3-connected minor of M. We say that a pair is N-deta...
Matroids were introduced in 1935 by Hassler Whitney to provide a way to abstractly capture the depen...
Robertson and Seymour constructed for every graph $G$ a tree-decomposition that efficiently distingu...
We apply a recent tangle-tree duality theorem in abstract separation systems to derive tangle-tree-t...
Originally, tangles were invented as an abstract tool in mathematical graph theory to prove the famo...
We establish a connection between tangles, a concept from structural graph theory that plays a centr...
A tangle in a matroid is an obstruction to small branch-width. In particular, the maximum order of ...
We study arrangements of slightly skewed tropical hyperplanes, called blades by A. Ocneanu, on the v...
This article describes the notion of branch-width and its dual notion, tangles. Branch-width was int...
This is the author accepted manuscript. The final version is available from Elsevier via http://dx.d...
A tangle of order k in a connectivity function λ may be thought of as a "k-connected component" of λ...
A tangle in a matroid is an obstruction to small branch-width. In particular, the maximum order of a...
The classical tool at the matroid theorist’s disposal when dealing with the common problem of wantin...
The authors showed in an earlier paper that there is a tree that displays, up to a natural equivalen...
AbstractA tangle in a matroid is an obstruction to small branch-width. In particular, the maximum or...
Let M be a 3-connected matroid, and let N be a 3-connected minor of M. We say that a pair is N-deta...
Matroids were introduced in 1935 by Hassler Whitney to provide a way to abstractly capture the depen...
Robertson and Seymour constructed for every graph $G$ a tree-decomposition that efficiently distingu...
We apply a recent tangle-tree duality theorem in abstract separation systems to derive tangle-tree-t...
Originally, tangles were invented as an abstract tool in mathematical graph theory to prove the famo...
We establish a connection between tangles, a concept from structural graph theory that plays a centr...
A tangle in a matroid is an obstruction to small branch-width. In particular, the maximum order of ...
We study arrangements of slightly skewed tropical hyperplanes, called blades by A. Ocneanu, on the v...
This article describes the notion of branch-width and its dual notion, tangles. Branch-width was int...
This is the author accepted manuscript. The final version is available from Elsevier via http://dx.d...
A tangle of order k in a connectivity function λ may be thought of as a "k-connected component" of λ...
A tangle in a matroid is an obstruction to small branch-width. In particular, the maximum order of a...
The classical tool at the matroid theorist’s disposal when dealing with the common problem of wantin...
The authors showed in an earlier paper that there is a tree that displays, up to a natural equivalen...
AbstractA tangle in a matroid is an obstruction to small branch-width. In particular, the maximum or...
Let M be a 3-connected matroid, and let N be a 3-connected minor of M. We say that a pair is N-deta...
Matroids were introduced in 1935 by Hassler Whitney to provide a way to abstractly capture the depen...
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