Subgraphs of random graphs with specified degrees

@inproceedings{McKay2011SubgraphsOR,
  title={Subgraphs of random graphs with specified degrees},
  author={Brendan D. McKay},
  year={2011}
}
  • B. McKay
  • Published 1 June 2011
  • Mathematics
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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This work proves some basic facts about the structure of a random graph with degree sequence d, including the probability of a given subgraph or induced subgraph, using the multidimensional saddle-point method.
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Random dense bipartite graphs and directed graphs with specified degrees
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The uniform distribution on the space of simple bipartite graphs with degree sequence S in one part and T in the other is studied; equivalently, binary matrices with row sums S and column sums T are studied.
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