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In general graphs

In general graphs, 2 n – 1 matchings are no longer sufficient. When n is even, one can add to Drisko's example the matching { (x, x), (y, y), (x, x), (y, y), … } and get a family of 2 n – 1 matchings without any rainbow matching.

Aharoni, Berger, Chudnovsky, Howard and Seymour proved that, in a general graph, 3 n – 2 matchings (=colors) are always sufficient. It is not known whether this is tight: currently the best lower bound for even n is 2 n and for odd n it is 2 n – 1.