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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

A coarse-geometry characterization of cacti

Koji Fujiwara , Panos Papasoglu This is my paper
classification math.MG math.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 3 Pith papers

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

  1. Asymptotic structure. III. Excluding a fat tree

    math.CO 2025-09 conditional novelty 8.0

    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.

  2. Coarse Menger property of quasi-minor excluded graphs and length spaces

    math.CO 2026-05 unverdicted novelty 7.0

    Locally finite graphs with an excluded finite minor have the weak coarse Menger property with f depending only on k and g linear in r independent of k.

  3. A coarse block-cutvertex tree-decomposition

    math.CO 2026-07 accept novelty 6.0

    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.