Expansion Of Product Replacement Graphs

We establish a connection between the expansion coefficient of the product replacement graph Γ k (G) and the minimal expansion coefficient of a Cayley graph of G with k generators. In particular, we show that the product replacement graphs Γ k (PSL(2,p)) form an expander family, under assumption that all Cayley graphs of PSL(2,p), with at most k generators are expanders. This gives a new explanation of the outstanding performance of the product replacement algorithm and supports the speculation that all product replacement graphs are expanders [42,52].

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Correspondence to Alexander Gamburd.

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Gamburd, A., Pak, I. Expansion Of Product Replacement Graphs. Combinatorica 26, 411–429 (2006). https://doi.org/10.1007/s00493-006-0023-0

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Mathematics Subject Classification (2000):

  • 05C90
  • 68R10
  • 20F99