Year: 2025
Type: article
Abstract: ABSTRACT Carmesin and Gollin proved that every finite graph has a canonical tree‐decomposition of adhesion less than that efficiently distinguishes every two distinct ‐profiles, and which has the further property that every separable ‐block is equal to the unique part of in which it is contained. We give a shorter proof of this result by showing that such a tree‐decomposition can in fact be obtained from any canonical tight tree‐decomposition of adhesion less than . For this, we decompose the parts of such a tree‐decomposition by further tree‐decompositions. As an application, we also obtain a generalization of Carmesin and Gollin's result to locally finite graphs.
Source: Journal of Graph Theory
DOI: 10.1002/jgt.23230
Author: Sandra Albrechtsen
Institution: Universität Hamburg
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $4,150
OpenAlex ID: W4407371655