On the number of large h-hypergraphs with a fixed diameter Original Research Article

An asymptotic formula for the number of labeled h-hypergraphs of order n and diameter equal to k, denoted by H(n,h;d=k) is found as n→∞ for every h⩾3 and k⩾2. This depends on the parity of k and is more precise for k⩾5. As a consequence, it is deduced that for every fixed h⩾3 and k⩾1, limn→∞ H(n,h;d=k)/H(n,h;d=k+1)=∞ holds, thus extending the corresponding results for graphs and digraphs.