Subgraphs of random graphs with specified degrees

If a graph is chosen uniformly at random from all the graphs with a given degree sequence, what can be said about its subgraphs? The same can be asked of bipartite graphs, equivalently 0-1 matrices. These questions have been studied by many people. In this paper we provide a partial survey of the eld, with emphasis on two general techniques: the method of switchings and the multidimensional saddle-point method.

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