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 \documentclass{article}\pagestyle{empty}\begin{document}$\mathop {\lim }\limits_{n \to \infty } r/n = \lambda$\end{document} and \documentclass{article}\pagestyle{empty}\begin{document}$\mathop {\lim }\limits_{n \to \infty } s/n = \mu$\end{document} . Also, some estimations of the number of subtrees for almost all graphs are made by using Chebycheff's inequality. © 1994 John Wiley & Sons, Inc.