Year: 2026
Type: article
Abstract: 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 ∈ ℕ , every tree-decomposition of a graph G which efficiently distinguishes all its k -tangles can be refined to a tree-decomposition whose parts are either too small to be home to a k -tangle, or as small as possible while being home to a k -tangle.
Source: Innovations in Graph Theory
DOI: 10.5802/igt.21
Author: Sandra Albrechtsen
Institution: Universität Hamburg
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W7148500440