Quasi‐random graphs with given degree sequences

It is now known that many properties of the objects in certain combinatorial structures are equivalent, in the sense that any object possessing any of the properties must of necessity possess them all. These properties, termed quasirandom, have been described for a variety of structures such as graphs, hypergraphs, tournaments, Boolean functions, and subsets of Z _n, and most recently, sparse graphs. In this article, we extend these ideas to the more complex case of graphs which have a given degree sequence. © 2007 Wiley Periodicals, Inc. Random Struct. Alg., 2008