English

Paths in graphs: bounded geometry and property A

Metric Geometry 2025-11-21 v1

Abstract

We expose a class of discrete metric spaces, for which bounded geometry is equivalent to the property A of G. Yu. This class includes the coarse disjoint union of (Z/2Z)n(\mathbb Z/2\mathbb Z)^n, nNn\in\mathbb N, and consists of spaces of simple paths in a class of graphs that includes cactus graphs, with the metric defined as the number of edges in the symmetric difference of the paths. We also show that if a space in this class does not have bounded geometry then it contains a subspace of bounded geometry without property A.

Keywords

Cite

@article{arxiv.2511.15855,
  title  = {Paths in graphs: bounded geometry and property A},
  author = {V. Manuilov},
  journal= {arXiv preprint arXiv:2511.15855},
  year   = {2025}
}

Comments

9 pages

R2 v1 2026-07-01T07:46:09.966Z