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.
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
a set of pairwise non-adjacent edges
a subgraph of the folding graph in which no vertex is connected to more than one other vertex
a subset of the edges of G such that no two edges of the subset are adjacent in G