On the separation profile of infinite graphs

  • Itai Benjamini

    Weizmann Institute of Science, Rehovot, Israel
  • Oded Schramm

    Redmond, USA
  • Ádám Timár

    Universität Bonn, Germany

Abstract

Initial steps in the study of inner expansion properties of infinite Cayley graphs and other infinite graphs, such as hyperbolic ones, are taken, in a flavor similar to the well-known Lipton–Tarjan n\sqrt{n} separation result for planar graphs. Connections to relaxed versions of quasi-isometries are explored, such as regular and semiregular maps.

Cite this article

Itai Benjamini, Oded Schramm, Ádám Timár, On the separation profile of infinite graphs. Groups Geom. Dyn. 6 (2012), no. 4, pp. 639–658

DOI 10.4171/GGD/168