It is known, that maximal matchings (i.e. matchings with the maximal number of edges) and optimal matchings (i.e. matchings for which the sum of edge weights is optimal) can be calculated in polynomial time.
I would like to know whether the same is true for optimal matchings with a given fixed number of edges.
The problem can be illustrated as follows: a tennis club has the task to find e.g. the 10 best pairs of players that will take part in a tournament of doubles (i.e. two players on each side). The situation can be modeled as a graph where the vertices correspond to players and the edge weights correspond to the playing strength of the pair of players. The task is then to find 10 non-adjacent edges with maximal weight sum.