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.
Original language | English (US) |
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Pages (from-to) | 1241-1256 |
Number of pages | 16 |
Journal | Proceedings of the American Mathematical Society |
Volume | 143 |
Issue number | 3 |
DOIs | |
State | Published - 2015 |
All Science Journal Classification (ASJC) codes
- General Mathematics
- Applied Mathematics