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 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. 639–658DOI 10.4171/GGD/168