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On Local Expansion of Vertex-Transitive Graphs
Published online by Cambridge University Press: 01 June 1998
Abstract
Let X be a vertex-transitive graph and let S be an arbitrary finite subset of its vertices. Denote by @∂S the set of vertices adjacent to S but not in S. Babai and Szegedy proved that for an infinite, connected, locally finite X with subexponential growth we have
formula here
where d(S) is the diameter of S. The aim of this note is to provide a slightly better, tight lower bound on this quantity. We prove that
formula here
under the same conditions.
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- 1998 Cambridge University Press
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