7 citations · 11 across the 11 of their papers we have counts for
13 papers
Proof of Lichiardopol's conjecture on disjoint directed cycles of distinct lengths
Sandra Albrechtsen, Raphael Steiner
There is a fascinating array of interrelated questions studying which structures can be guaranteed in digraphs of large minimum out-degree. These often have intriguingly simple sta…
Locally interval graphs are circular-arc graphs
Tara Abrishami, Sandra Albrechtsen, Nathan Bowler +2
Circular-arc graphs are graphs that can be represented as intersection graphs of subpaths of a cycle. Interval graphs are graphs that can be represented as intersection graphs of s…
Displaying prescribed sets of ends by linked tree-decompositions
Sandra Albrechtsen, Max Pitz, Roman Schaut
We show that if a subset of the ends of a graph can be displayed by a tree-decomposition of finite adhesion, then it can also be displayed by a linked such tree-decompositi…
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…
A structural duality for path-decompositions into parts of small radius
Sandra Albrechtsen, Reinhard Diestel, Ann-Kathrin Elm +4
It is an easy observation that if a graph~ admits a path-decomposition whose parts have small radius, then contains no large subdivision of or as a (quasi-)g…
A Menger-type theorem for two induced paths
Sandra Albrechtsen, Tony Huynh, Raphael W. Jacobs +2
We give an approximate Menger-type theorem for when a graph contains two paths and such that is an induced subgraph of . More generally, we…
Optimal trees of tangles: refining the essential parts
Sandra Albrechtsen
We combine the two fundamental fixed-order tangle theorems of Robertson and Seymour into a single theorem that implies both, in a best possible way. We show that, for every $k \in…
Refining trees of tangles in abstract separation systems: inessential parts
Sandra Albrechtsen
Robertson and Seymour proved two fundamental theorems about tangles in graphs: the tree-of-tangles theorem, which says that every graph has a tree-decomposition such that distingui…