On random symmetric travelling salesman problems

Let the edges of the complete graph K_n be assigned independent uniform [0,1] random edge weights. Let Z_TSP and Z_2FAC be the weights of the minimum length travelling salesman tour and minimum weight 2-factor respectively. We show that whp¹ |Z_TSP-Z_2FAC|=(1). The proof is via the analysis of a polynomial time algorithm that finds a tour only a little longer than Z_2FAC.