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A directed cycle-cover of a digraph $D$ is in the sense of this post equivalent to a perfect matching in the related undirected biadjacency graph $B$ in which the edges connect a vertex $u$ of $D$ in ...

Permanents can be interpreted as counting directed cycle covers of an asymmetric graph with unit cost edge weights. That interpretation leads to a branch and bound algorithm for calculating the ...

We can find Pfaffian orientation and take determinant to compute permanent in $O(n^\omega)$ time where $\omega$ is exponent of matrix multiplication. We know that permanent of $O(n)$ vertex planar ...