7 citations · 11 across the 11 of their papers we have counts for
4 papers · 1 filter
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…