Expansion of Product Replacement Graphs (2001)
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| Venue: | Combinatorica |
| Citations: | 8 - 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].
