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 separation result for planar graphs. Connections to relaxed versions of quasi-isometries are explored, such as regular and semiregular maps.
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Benjamini et al. (2012) studied this question.
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