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arXiv · 2501.10840

Graphs that are quasi-isometric to graphs with bounded treewidth

Robert Hickingbotham
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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.

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Robert Hickingbotham. 2025-08-20. Graphs that are quasi-isometric to graphs with bounded treewidth. https://arxiv.org/abs/2501.10840

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