Work

A structural duality for path-decompositions into parts of small radius

Year: 2026

Type: article

Abstract: It is an easy observation that if a graph G admits a path-decomposition whose parts have small radius, then G contains no large subdivision of K 1 , 3 or K 3 as a (quasi-)geodesic subgraph. We show that these are in fact the only obstructions to such path-decompositions of small radial width, and we prove analogous results for decompositions modelled on cycles and subdivided stars instead of paths. With our results we confirm in a strong form a conjecture of Georgakopoulos and Papasoglu on fat-minor-characterisations of graphs quasi-isometric to paths, cycles and paths, and subdivided stars, respectively. For this, we present a novel view on quasi-isometries between graphs by graph-decompositions of bounded radial width and spread. This new perspective enables us to prove further results in coarse graph theory, and may thus be of independent interest.

Source: Innovations in Graph Theory

DOI: 10.5802/igt.22

Authors: Sandra Albrechtsen, Reinhard Diestel, Ann-Kathrin Elm, Eva Fluck, Raphael W. Jacobs, Paul Knappe, Paul Wollan

Institutions: Universität Hamburg, Heidelberg University, RWTH Aachen University, Sapienza University of Rome

Language: English

Topic: Advanced Graph Theory Research

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: diamond

Funder: Studienstiftung des Deutschen Volkes

OpenAlex ID: W4384648187

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