I use the following to iterate over all matchings and perfect matchings.
def matchings(G):
edges = G.edges(labels = False)
verts = [[v] for v in G]
m = len(edges)
for match in DLXCPP(edges+verts):
yield [edges[t] for t in match if t < m]
def perfect_matchings(G):
edges = G.edges(labels = False)
for match in DLXCPP(edges):
yield [edges[t] for t in match]
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