On Local Expansion of Vertex-Transitive Graphs

Authors:
András Lukács
Affiliations:
Computer and Automation Research Institute, Hungarian Academy of Sciences, MTA SZTAKI, Lágymányosi u. 11., H-1111 Budapest, Hungary (e-mail: lukacs@cs.elte.hu)
Venue:
Combinatorics, Probability and Computing
Year:
1998

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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***** Insert equation 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***** Insert equation here *****under the same conditions.