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].

This is a preview of subscription content, access via your institution.

Author information



Corresponding author

Correspondence to Alexander Gamburd.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

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

Download citation

Mathematics Subject Classification (2000):

  • 05C90
  • 68R10
  • 20F99