Efficiently distinguishing all tangles in locally finite graphs

Raphael W. JacobsPaul Knappe

Mar 2023

摘要

While finite graphs have tree-decompositions that efficiently distinguish alltheir tangles, locally finite graphs with thick ends need not have suchtree-decompositions. We show that every locally finite graph without thick endsadmits such a tree-decomposition, in fact a canonical one. Our proof exhibits athick end at any obstruction to the existence of such tree-decompositions andbuilds on new methods for the analysis of the limit behaviour of strictlyincreasing sequences of separations.

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