Random matching problems on the complete graph

The edges of the complete graph on n vertices are assigned independent exponentially distributed costs. A k-matching is a set of k edges of which no two have a vertex in common. We obtain explicit bounds on the expected value of the minimum total cost C-k,C-n of a k-matching. In particular we prove that if n = 2k then pi(2)/12 < ECk,n < pi(2)/12 + log n/n.