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Complexity of heaviest 2-optimal vertex-disjoint cycle covers

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 ...
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Matching of two weighted graphs allowing one-to-many mapping

I am looking for a heuristic for a graph matching problem as follows. Given two graphs: $A$ (consisting of nodes $a_i$) and $B$ (consisting of nodes $b_i$). Typically the size of $B$ is larger than ...