Quasi-isometries between graphs and trees |
| |
Authors: | Bernhard Krn Rgnvaldur G Mller |
| |
Institution: | aUniversity of Vienna, Faculty of Mathematics, Nordbergstraße 15, 1090 Wien, Austria;bScience Institute, University of Iceland, Dunhaga 3, 107 Reykjavik, Iceland |
| |
Abstract: | 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. |
| |
Keywords: | Quasi-isometry Tree Ends of graphs d-fiber Quasi-geodesic |
本文献已被 ScienceDirect 等数据库收录! |
|