Efficiently distinguishing all tangles in locally finite graphs
Combinatorics
2024-03-25 v2
Abstract
While finite graphs have tree-decompositions that efficiently distinguish all their tangles, locally finite graphs with thick ends need not have such tree-decompositions. We show that every locally finite graph without thick ends admits such a tree-decomposition, in fact a canonical one. Our proof exhibits a thick end at any obstruction to the existence of such tree-decompositions and builds on new methods for the analysis of the limit behaviour of strictly increasing sequences of separations.
Cite
@article{arxiv.2303.09332,
title = {Efficiently distinguishing all tangles in locally finite graphs},
author = {Raphael W. Jacobs and Paul Knappe},
journal= {arXiv preprint arXiv:2303.09332},
year = {2024}
}
Comments
19 pages, new revised version: fixed several small typos, included appendix into main body of the paper, added new proof of Lemma 3.10, added two figures and fixed proof of Lemma 4.5