SPANNING TREE PROBLEM

Dept. of Computer 'Science and Statistics, Queen Mary College, Mile End Road, London E1 4NS, England Received 23 February 1983 Revised 13 April 1984 Suppose we are given a complete graph on n vertices in which the lengths of the edges are in- dependent identically distributed non-negative random variables. Suppose that their common distribution function F is differentiable at zero and D = F'(0)> 0 and each edge length has a finite mean and variance. Let L n be the random variable whose value is the length of the minimum spanning tree in such a graph. Then we will prove the following: lim n ~ ~ E(Ln)= ((3)/D where (( 3)=