Perfect matchings as IID factors on non-amenable groups

Perfect matchings as IID factors on non-amenable groups

We prove that in every bipartite Cayley graph of every non-amenable group, there is a perfect matching that is obtained as a factor of independent uniform random variables. We also discuss expansion properties of factors and improve the Hoffman spectral bound on the independence number of finite gra...

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Veröffentlicht in:European journal of combinatorics 2011-10, Vol.32 (7), p.1115-1125
Hauptverfasser: Lyons, Russell, Nazarov, Fedor
Format: Artikel
Sprache:eng
Schlagworte:
Combinatorial analysis
Graphs
Matching
Mathematical analysis
Random variables
Spectra
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Zusammenfassung:We prove that in every bipartite Cayley graph of every non-amenable group, there is a perfect matching that is obtained as a factor of independent uniform random variables. We also discuss expansion properties of factors and improve the Hoffman spectral bound on the independence number of finite graphs.
ISSN:0195-6698
1095-9971
DOI:10.1016/j.ejc.2011.03.008