Pancyclic out-arcs of a vertex in tournaments

Thomassen (J. Combin. Theory Ser. B 28, 1980, 142-163) proved that every st rong tournament contains a vertex x such that each are going out from x is contained in a Hamiltonian cycle. In this paper, we extend the result of Th omassen and prove that a strong tournament contains a vertex x such that ev ery are going out from x is pancyclic, and our proof yields a polynomial al gorithm to find such a vertex. Furthermore, as another consequence of our m ain theorem, we get a result of Alspach (Canad. Math. Bull. 10, 1967, 283-2 86) that states that every are of a regular tournament is pancyclic. (C) 20 00 Elsevier Science B.V. All rights reserved.