Uniform approximation of metrics by graphs
Metric Geometry
2013-06-25 v2
Abstract
We say that a metric graph is uniformly bounded if the degrees of all vertices are uniformly bounded and the lengths of edges are pinched between two positive constants; a metric space is approximable by a uniform graph if there is one within a finite Gromov-Hausdorff distance. We show that the Euclidean plane and Gromov hyperbolic geodesic spaces with bounded geometry are approximable by uniform graphs, and pose a number of open problems.
Cite
@article{arxiv.1210.2435,
title = {Uniform approximation of metrics by graphs},
author = {Dmitri Burago and Sergei Ivanov},
journal= {arXiv preprint arXiv:1210.2435},
year = {2013}
}
Comments
15 pages, v2: improved introduction and corrected some formulae