Regular pairs in sparse random graphs I

Authors:
Y. Kohayakawa;V. Rödl
Affiliations:
Instituto de Matemática e Estatística, Universidade de São Paulo, Rua do Matão, 1010, 05508-090 São Paulo, Brazil;Department of Mathematics and Computer Science, Emory University, Atlanta, Georgia
Venue:
Random Structures & Algorithms
Year:
2003

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Abstract

We consider bipartite subgraphs of sparse random graphs that are regular in the sense of Szemerédi and, among other things, show that they must satisfy a certain local pseudorandom property. This property and its consequences turn out to be useful when considering embedding problems in subgraphs of sparse random graphs.