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 , , 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}
}
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9 pages