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We introduce a " derandomized " analogue of graph squaring. This operation increases the connectivity of the graph (as measured by the second eigenvalue) almost as well as squaring the graph does, yet only increases the degree of the graph by a constant factor, instead of squaring the degree. One application of this product is an alternative proof of… (More)

We describe here a simple probabilistic model for graphs that are lifts of a fixed base graph <i>G</i>, i.e., those graphs from which there is a covering man onto <i>G</i>. Our aim is to investigate the properties of typical graphs in this class. In particular, we show that almost every lift of <i>G</i> is δ(<i>G</i>)-connected where δ(<i>G</i>)… (More)

We assume that for some <i>fixed</i> large enough integer d, the symmetric group S<inf>d</inf> can be generated as an expander using d<sup>1/30</sup> generators. Under this assumption, we explicitly construct an infinite family of groups G<inf>n</inf>, and explicit sets of generators Y<inf>n</inf> ⊂ G<inf>n</inf>, such that all generating sets have… (More)

We construct a sequence of groups G n , and explicit sets of generators Y n ⊂ G n , such that all generating sets have bounded size, and the associated Cayley graphs are all expanders. The group G 1 is the alternating group A d , the set of even permutations on the elements {1, 2,. .. , d}. The group G n is the group of all even symmetries of the rooted… (More)

- Salil P. Vadhan, Luca Trevisan, Omer Reingold, Boaz Barak, Eli Ben-Sasson, Michael Capalbo +55 others
- 2012

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