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arXiv · 1210.2435

Uniform approximation of metrics by graphs

Dmitri Burago·Sergei Ivanov
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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.

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Dmitri Burago, Sergei Ivanov. 2013-06-23. Uniform approximation of metrics by graphs. https://arxiv.org/abs/1210.2435

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