## Expansion of Product Replacement Graphs (2001)

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Venue: | Combinatorica |

Citations: | 9 - 1 self |

### BibTeX

@TECHREPORT{Gamburd01expansionof,

author = {Alexander Gamburd and Igor Pak},

title = {Expansion of Product Replacement Graphs},

institution = {Combinatorica},

year = {2001}

}

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### Abstract

. We establish a connection between the expansion coefficient of the product replacement graph \Gamma 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 \Gamma k \Gamma PSL(2; p) \Delta 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 [LP,P3].