Graphs that are quasi-isometric to graphs with bounded treewidth
Abstract
In this paper, we characterise graphs that are quasi-isometric to graphs with bounded treewidth. Specifically, we prove that a graph is quasi-isometric to a graph with bounded treewidth if and only if it has a tree-decomposition where each bag consists of a bounded number of balls of bounded diameter. This result extends a characterisation by Berger and Seymour (2024) of graphs that are quasi-isometric to trees. Additionally, we characterise graphs that are quasi-isometric to graphs with bounded pathwidth and graphs that are quasi-isometric to graphs with bounded linewidth. As an application of these results, we show that graphs with bounded rank-width, graphs with bounded tree independence number, and graphs with bounded sim-width are quasi-isometric to graphs with bounded treewidth.
Keywords
Cite
@article{arxiv.2501.10840,
title = {Graphs that are quasi-isometric to graphs with bounded treewidth},
author = {Robert Hickingbotham},
journal= {arXiv preprint arXiv:2501.10840},
year = {2025}
}