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

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Algorithms - ESA’ 99 (ESA 1999)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1643))

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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 Γ (G,S). We show that for almost all choices of S given k = 2alog2 |G|, a > 1, we have Reλ1 ≤ 1-1/2a. A similar but weaker result was obtained earlier by Alon and Roichman (see [4]).

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References

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Author information

Authors and Affiliations

  1. Department of Mathematics, Yale University, New Haven, CT, 06520

    Igor Pak

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  1. Igor Pak
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Editors and Affiliations

  1. Department of Applied Mathematics and DIMATIA Centre, Charles University, Malostranská nám. 25, CZ-11800, Prague 1, Czech Republic

    Jaroslav Nešetřil

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Pak, I. (1999). Random Cayley Graphs with O(log|G|) Generators Are Expanders. In: Nešetřil, J. (eds) Algorithms - ESA’ 99. ESA 1999. Lecture Notes in Computer Science, vol 1643. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48481-7_45

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  • DOI: https://doi.org/10.1007/3-540-48481-7_45

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  • Print ISBN: 978-3-540-66251-8

  • Online ISBN: 978-3-540-48481-3

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