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A perfect matching is a matching of all the vertices of a graph. In other words, a perfect matching is a set of edges such that each vertex of the graph is incident to exactly one edge in the set.

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Applications of Perfect Matching

Perfect matching is used in combinatorial optimisation / constraint satisfaction for the AllDifferent constraint. Given a set of variables $x_1, \dots, x_n$ with domains $X_1, \dots, X_n \subset A$ fi …
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