
An Efficient Algorithm for Enumerating Chordal Bipartite Induced Subgraphs in Sparse Graphs
In this paper, we propose a characterization of chordal bipartite graphs...
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Fast uniform generation of random graphs with given degree sequences
In this paper we provide an algorithm that generates a graph with given ...
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Counting independent sets in graphs with bounded bipartite pathwidth
We show that a simple Markov chain, the Glauber dynamics, can efficientl...
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Existence and polynomial time construction of biregular, bipartite Ramanujan graphs of all degrees
We prove that there exist bipartite, biregular Ramanujan graphs of every...
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Uniform generation of spanning regular subgraphs of a dense graph
Let H_n be a graph on n vertices and let H_n denote the complement of H_...
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Asymptotic enumeration of digraphs and bipartite graphs by degree sequence
We provide asymptotic formulae for the numbers of bipartite graphs with ...
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BIG sampling
Graph sampling is a statistical approach to study real graphs, which rep...
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Sampling hypergraphs with given degrees
There is a wellknown connection between hypergraphs and bipartite graphs, obtained by treating the incidence matrix of the hypergraph as the biadjacency matrix of a bipartite graph. We use this connection to describe and analyse a rejection sampling algorithm for sampling simple uniform hypergraphs with a given degree sequence. Our algorithm uses, as a black box, an algorithm 𝒜 for sampling bipartite graphs with given degrees, uniformly or nearly uniformly, in (expected) polynomial time. The expected runtime of the hypergraph sampling algorithm depends on the (expected) runtime of the bipartite graph sampling algorithm 𝒜, and the probability that a uniformly random bipartite graph with given degrees corresponds to a simple hypergraph. We give some conditions on the hypergraph degree sequence which guarantee that this probability is bounded below by a constant.
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