Pancyclism and Meyniel's conditions (Q1071026)

\textit{H. Meyniel} [J. Comb. Theory, Ser. B 14, 137-147 (1973; Zbl 0259.05114)] has shown that a digraph of order n is Hamiltonian if for each pair of non adjacent vertices the degree sum is at least 2n-1. In accordance with \textit{J. A. Bondy's} metaconjecture [Proc. 2nd Louisiana Conf. Comb., Graph Theory, Comput., Baton Rouge, 161-172 (1971; Zbl 0291.05109)] the author proves that a digraph satisfying the same condition is pancyclic excepted if it is of one of 4 precised types. This result generalizes previous results obtained by Overbeck-Larish and Thomassen by considering stronger conditions on the degree sum of nonadjacent vertices.