### 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) |
---|---|

Pages (from-to) | 1241-1256 |

Number of pages | 16 |

Journal | Proceedings of the American Mathematical Society |

Volume | 143 |

Issue number | 3 |

DOIs | |

State | Published - Jan 1 2015 |

### All Science Journal Classification (ASJC) codes

- Mathematics(all)
- Applied Mathematics

## Fingerprint Dive into the research topics of 'Uniform approximation of metrics by graphs'. Together they form a unique fingerprint.

## Cite this

Burago, D., & Ivanov, S. (2015). Uniform approximation of metrics by graphs.

*Proceedings of the American Mathematical Society*,*143*(3), 1241-1256. https://doi.org/10.1090/s0002-9939-2014-12299-4