Accessibility, planar graphs, and quasi-isometries

2023/10/23 by Joseph MacManus, MacManus, Joseph · 1 citation
Computer Science · Mathematics · #20E08 #20F65 (Primary) 05C10 #51F30 (Secondary) #Combinatorics (math.CO) #Computational Geometry and Mesh Generation #FOS: Mathematics #Geometric and Algebraic Topology #Group Theory (math.GR) #Mathematics and Applications #Metric Geometry (math.MG)

paper · pdf · doi:10.48550/arxiv.2310.15242

openalex publication_date 2023/10/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that a connected, locally finite, quasi-transitive graph which is quasi-isometric to a planar graph is necessarily accessible. This leads to a complete classification of the finitely generated groups which are quasi-isometric to planar graphs. In particular, such a group is virtually a free product of free and surface groups, and thus virtually admits a planar Cayley graph.

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• String graphs are quasi-isometric to planar graphs

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