Asymptotic formulas for the number of oriented graphs

AbstractWille found an asymptotic approximation to r(n, q), the number of unlabeled oriented graphs on n points and q directed lines, for a wide interval of q and conjectured that, for given n, the maximum of r(n, q) occurs at q = [2(N + 1)3]. We find the (different) asymptotic approximation to r(n, q) valid for the remaining interval of q and prove Wille's conjecture for all large n