Quasi-isometries between graphs and trees

Bernhard Krön, Rögnvaldur G. Möller

Research output: Contribution to journalArticlepeer-review

6 Citations (Scopus)

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.

Original languageEnglish
Pages (from-to)994-1013
Number of pages20
JournalJournal of Combinatorial Theory. Series B
Volume98
Issue number5
DOIs
Publication statusPublished - Sep 2008

Other keywords

  • d-fiber
  • Ends of graphs
  • Quasi-geodesic
  • Quasi-isometry
  • Tree

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