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A matching in a graph is a set of edges such that every vertex of the graph is on at most one edge in the set.
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a set of edges in a (bipartite) graph on vertex set X Y such that none of them have a vertex in common with any of the others
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a set of pairwise non-adjacent edges
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a subgraph of the folding graph in which no vertex is connected to more than one other vertex
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a subset of the edges of G such that no two edges of the subset are adjacent in G
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