Random matching problems on the complete graph

Artikel i vetenskaplig tidskrift, 2008

The edges of the complete graph on n vertices are assigned independent exponentially dis- tributed 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 Ck,n of a k-matching. In particular we prove that if n = 2k then π2 /12 < ECk,n < π2 /12 + log n/n.