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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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Symmetric matching in special graphs
Let $G$ be a bipartite graph, $L$ ($R$) be the set of vertices in the left (right) part.
Consider a graph $T$ with the set of vertices $R \times L$ ( $L \times R$ ) in the left (right) part. For any $ …