## Spanning trees in hyperbolic graphs

- Matthias Hamann
- Combinatorica
- 2016

1 Excerpt

- Published 2008 in J. Comb. Theory, Ser. B

Criteria for quasi-isometry between trees and general graphs as well as for quasi-isometries between metrically almost transitive graphs and trees are found. Thereby we use different concepts of thickness for graphs, ends and end spaces. A metrically almost transitive graph is quasi-isometric to a tree if and only if it has only thin metric ends (in the sense of Definition 3.6). If a graph is quasi-isometric to a tree then there is a one-to-one correspondence between the metric ends and those d-fibers which contain a quasi-geodesic. The graphs considered in this paper are not necessarily locally finite. © 2007 Elsevier Inc. All rights reserved.

@article{Krn2008QuasiisometriesBG,
title={Quasi-isometries between graphs and trees},
author={Bernhard Kr{\"{o}n and R{\"{o}gnvaldur G. M{\"{o}ller},
journal={J. Comb. Theory, Ser. B},
year={2008},
volume={98},
pages={994-1013}
}