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A perfect 2-matching of a graph is a vector assigning values 0,1, or 2 to the edges such that the sum of values of edges incident with any node is equal to 2. For restricted perfect 2-matchings, we are also given a collection of “allowed” odd cycles, and restrict ourselves to those perfect 2-matchings the support of which contains no odd cycle not in this collection. Given a graph and a collection...
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