Erdős-Rényi Sequences and Deterministic Construction of Expanding Cayley Graphs

  • Vikraman Arvind
  • Partha Mukhopadhyay
  • Prajakta Nimbhorkar
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7256)


Given a finite group G by its multiplication table, we give a deterministic polynomial-time construction of a directed O(log|G|) degree Cayley expander for G. Our construction exploits the connection between rapid mixing random walks and spectral expansion. Our main group-theoretic tool is Erdős-Rényi sequences. We give a similar construction of O(log|G|) degree undirected Cayley expanders for G, which is an alternative proof of Wigderson and Xiao’s derandomization [WX08] of the Alon-Roichman randomized construction.


Cayley Graph Random Element Expander Graph Distinct Index Ramanujan Graph 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Vikraman Arvind
    • 1
  • Partha Mukhopadhyay
    • 2
  • Prajakta Nimbhorkar
    • 2
  1. 1.The Institute of Mathematical SciencesChennaiIndia
  2. 2.Chennai Mathematical InstituteSiruseriIndia

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