We obtain an asymptotic formula for A n,q, the number of digraphs with n labeled vertices, q edges and no cycles. The derivation consists of two separate parts. In the first we analyze the generating function for A n,q so as to obtain a central limit theorem for an associated probability distribution. In the second part we show combinatorially that A n,q is a smooth function of q. By combining these results, we obtain the desired asymptotic formula.
- AMS (1980) subject classification: 05C30, 05C20