Erdős-Rényi Sequences and Deterministic Construction of Expanding Cayley Graphs
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.
KeywordsCayley Graph Random Element Expander Graph Distinct Index Ramanujan Graph
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