7 citations · 14 across the 14 of their papers we have counts for
5 papers · 1 filter
Hitting cycles through prescribed vertices or edges
Nathan Bowler, Ebrahim Ghorbani, Florian Gut +2
We prove that for every set of vertices of a directed graph , the maximum number of vertices in contained in a collection of vertex-disjoint cycles in is at least th…
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…
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…