Abstract
We describe a common generalization of the weighted matching problem and the weighted matroid intersection problem. In this context we establish common generalizations of the main results on those two problems—polynomial-time solvability, min-max theorems, and totally dual integral polyhedral descriptions. New application of these results include a strongly polynomial separation algorithm for the convex hull of matchable sets of a graph, and a polynomial-time algorithm to compute the rank of a certain matrix of indeterminates.
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