Random Cayley Graphs with O(log[G]) Generators Are Expanders

Authors:
Igor Pak
Affiliations:
-
Venue:
ESA '99 Proceedings of the 7th Annual European Symposium on Algorithms
Year:
1999

Citing 1
Cited 1

Automorphism groups, isomorphism, reconstruction

Handbook of combinatorics (vol. 2)

Erdős-Rényi sequences and deterministic construction of expanding cayley graphs

LATIN'12 Proceedings of the 10th Latin American international conference on Theoretical Informatics

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Abstract

Let G be a finite group. Choose a set S of size k uniformly from G and consider a lazy random walk on the corresponding Cayley graph 驴(G,S). We show that for almost all choices of S given k = 2alog2 |G|, a 1, we have Re驴1 驴 1-1/2a. A similar but weaker result was obtained earlier by Alon and Roichman (see [4]).