Let the edges of the complete graph Kn be assigned independent uniform [0, 1] random edge weights. Let ZTSP and Z2FAC be the weights of the minimum length travelling salesman tour and minimum weight 2-factor, respectively. We show that whp |ZTSP − Z2FAC| = o(1). The proof is obtained by the analysis of a polynomial time algorithm that finds a tour only a little longer than Z2FAC.
