7 citations · 11 across the 11 of their papers we have counts for
6 papers · 1 filter
On vertex sets inducing tangles
Sandra Albrechtsen, Hanno von Bergen, Raphael W. Jacobs +2
Diestel, Hundertmark and Lemanczyk asked whether every -tangle in a graph is induced by a set of vertices by majority vote. We reduce their question to graphs whose size is boun…
A characterisation of graphs quasi-isometric to -minor-free graphs
Sandra Albrechtsen, Raphael W. Jacobs, Paul Knappe +1
We prove that there is a function such that every graph with no -fat minor is -quasi-isometric to a graph with no minor. This solves the -case of a ge…
Linked tree-decompositions into finite parts
Sandra Albrechtsen, Raphael W. Jacobs, Paul Knappe +1
We prove that every graph which admits a tree-decomposition into finite parts has a rooted tree-decomposition into finite parts that is linked, tight and componental. As an applica…
Tangle-tree duality in infinite graphs
Sandra Albrechtsen
We extend Robertson and Seymour's tangle-tree duality theorem to infinite graphs.
Counterexamples regarding linked and lean tree-decompositions of infinite graphs
Sandra Albrechtsen, Raphael W. Jacobs, Paul Knappe +1
Kriz and Thomas showed that every (finite or infinite) graph of tree-width admits a lean tree-decomposition of width . We discuss a number of counterexamples…
Refining tree-decompositions so that they display the k-blocks
Sandra Albrechtsen
Carmesin and Gollin proved that every finite graph has a canonical tree-decomposition of adhesion less than that efficiently distinguishes every two distinct…