On random symmetric travelling salesman problems

Let the edges of the complete graph K/sub n/ be assigned independent uniform [0,1] random edge weights. Let Z/sub TSP/ and Z/sub 2FAC/ be the weights of the minimum length travelling salesman tour and minimum weight 2-factor respectively. We show that whp/sup 1/ |Z/sub TSP/-Z/sub 2FAC/|=(1). The proof is via the analysis of a polynomial time algorithm that finds a tour only a little longer than Z/sub 2FAC/.