Groups, Geometry, and Dynamics

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Volume 6, Issue 4, 2012, pp. 639–658
DOI: 10.4171/GGD/168

Published online: 2012-11-10

On the separation profile of infinite graphs

Itai Benjamini[1], Oded Schramm[2] and Ádám Timár[3]

(1) Weizmann Institute of Science, Rehovot, Israel
(2) Redmond, USA
(3) Universität Bonn, Germany

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 $\sqrt{n}$ separation result for planar graphs. Connections to relaxed versions of quasi-isometries are explored, such as regular and semiregular maps.

Keywords: Separation, quasi-isometry, group property, asymptotic dimension

Benjamini Itai, Schramm Oded, Timár Ádám: On the separation profile of infinite graphs. Groups Geom. Dyn. 6 (2012), 639-658. doi: 10.4171/GGD/168