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Let $G(V,E)$ be a undirected graph. I am interested in the fastest known algorithm for counting the number of perfect matchings in $G(V,E)$ (which is known to be in $\#P$). In particular, what is the ...

Calculating lightest vertex-disjoint cycle covers of finite complete symmetric graphs with weighted edges can be done efficiently and also renders the edge set of the calculated cycles free of pairs ...