On the number of subtrees for almost all graphs

In this article it is shown that the number of common edges of two random subtrees of K_n having r and s vertices, respectively, has a Poisson distribution with expectation 2λμ if $mathop {lim }limits_{n to infty } r/n = lambda$ and $mathop {lim }limits_{n to infty } s/n = mu$. Also, some estimations of the number of subtrees for almost all graphs are made by using Chebycheff's inequality. © 1994 John Wiley & Sons, Inc.