
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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Finding Efficient Domination for P_8Free Bipartite Graphs in Polynomial Time
A vertex set D in a finite undirected graph G is an efficient dominating...
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From independent sets and vertex colorings to isotropic spaces and isotropic decompositions
In the 1970's, Lovász built a bridge between graphs and alternating matr...
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Counting independent sets in unbalanced bipartite graphs
We give an FPTAS for approximating the partition function of the hardco...
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Fast algorithms for general spin systems on bipartite expanders
A spin system is a framework in which the vertices of a graph are assign...
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Counting perfect matchings and the eightvertex model
We study the approximation complexity of the partition function of the e...
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Weighted, Bipartite, or Directed Stream Graphs for the Modeling of Temporal Networks
We recently introduced a formalism for the modeling of temporal networks...
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Counting weighted independent sets beyond the permanent
In a landmark paper, Jerrum, Sinclair and Vigoda (2004) showed that the permanent of any square matrix can be estimated in polynomial time. This computation can be viewed as approximating the partition function of edgeweighted matchings in a bipartite graph. Equivalently, this may be viewed as approximating the partition function of vertexweighted independent sets in the line graph of a bipartite graph. Line graphs of bipartite graphs are perfect graphs, and are known to be precisely the class of (claw, diamond, odd hole)free graphs. So how far does the result of Jerrum, Sinclair and Vigoda extend? We first show that it extends to (claw, odd hole)free graphs, and then show that it extends to the even larger class of (fork, odd hole)free graphs. Our techniques are based on graph decompositions, which have been the focus of much recent work in structural graph theory, and on structural results of Chvátal and Sbihi (1988), Maffray and Reed (1999) and Lozin and Milanič (2008).
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