How to compute a perfect matching in a general graph?

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If you just want a perfect matching, you can use:

sage: p = G.matching()

If you want to iterate over all parfect matching, you can use (but it might be very slow as it is a brute force approach):

sage: for p in G.perfect_matchings():
....:     blah

You should download the PDF documentation which is available here. On page 222 there are 3 listed:

1. matching() Return a maximum weighted matching of the graph represented by the list of its edges.
2. has_perfect_matching() Return whether this graph has a perfect matching
3. perfect_matchings() Return an iterator over all perfect matchings of the graph.

Clicking on each method will bring you to more instructions and examples.