Recursive construction for 3-regular expanders

Abstract

We present an algorithm which inn 3 (logn)3 time constructs a 3-regular expander graph onn vertices. In each step we substitute a pair of edges of the graph by a new pair of edges so that the total number of cycles of lengths=⌊clogn⌋ decreases (for some fixed absolute constantc). When we reach a local minimum in the number of cycles of lengths the graph is an expander.

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Ajtai, M. Recursive construction for 3-regular expanders. Combinatorica 14, 379–416 (1994). https://doi.org/10.1007/BF01302963

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AMS subject classification code (1991)

  • 05 C 38
  • 05 C 85