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A coarse-geometry characterization of cacti

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arxiv 2305.08512 v1 pith:DNP7SXKN submitted 2023-05-15 math.MG math.CO

Koji Fujiwara , Panos Papasoglu This is my paper · ORCID
classification math.MGmath.CO
keywords characterizationcactigivequasi-isometricanotherbottleneckcoarse-geometrycurves
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We give a quasi-isometric characterization of cacti, which is similar to Manning's characterization of quasi-trees by the bottleneck property. We also give another quasi-isometric characterization of cacti using fat theta curves.

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Cited by 4 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Quasi-isometries, contractions, and intersection graphs

    math.CO 2026-08 conditional novelty 8.0 of 10

    Quasi-planar graphs are exactly the iterated subdivision-cover-intersection-graphs of planar graphs.

  2. A graph-theoretical characterisation of subgroups of Thompson's group $V$

    math.GR 2026-08 accept novelty 8.0 of 10

    A finitely generated group embeds in Thompson's group V if and only if it is the transition group of a context-free graph, which rules out intermediate-growth groups and the Basilica and Hanoi Towers groups.

  3. Asymptotic structure. III. Excluding a fat tree

    math.CO 2025-09 conditional novelty 8.0 of 10

    Any graph lacking a c-fat tree minor can be quasi-isometrically approximated by a graph with line-width bounded in terms of the tree and c.

  4. A coarse block-cutvertex tree-decomposition

    math.CO 2026-07 accept novelty 6.0 of 10

    Every connected graph has a tree-decomposition with bounded-diameter adhesion sets and coarsely inseparable bags, yielding a metric analogue of the block-cutvertex tree.

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