Abstract: | A random mapping (T; q) of a finite set V = {1, 2,…,n} into itself assigns independently to each i ? V its unique image j = TT(i)E V with probability q for i = j and with probability $ frac{{1 - q}}{{n - 1}} $ for j ≠ i. The purpose of the article is to determine the asymptotic behaviour of the size of the largest connected component of the random digraph GT(q) representing thes mapping as n–x, regarding all possible values of the parameter q = q(n). © 1994 John Wiley & Sons, Inc. |