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Random dense bipartite graphs and directed graphs with specified degrees
[article]

2009
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arXiv
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pre-print

Let S and T be vectors of positive integers with the same sum. We study the uniform distribution on the space of simple bipartite graphs with degree sequence S in one part and T in the other; equivalently, binary matrices with row sums S and column sums T. In particular, we find precise formulae for the probabilities that a given bipartite graph is edge-disjoint from, a subgraph of, or an induced subgraph of a random graph in the class. We also give similar formulae for the uniform distribution

arXiv:math/0701600v5
fatcat:et3qj3iklfcjrkylfu47z5wgpm