Pancyclic out-arcs of a vertex in tournaments

AbstractThomassen (J. Combin. Theory Ser. B 28, 1980, 142–163) proved that every strong tournament contains a vertex x such that each arc going out from x is contained in a Hamiltonian cycle. In this paper, we extend the result of Thomassen and prove that a strong tournament contains a vertex x such that every arc going out from x is pancyclic, and our proof yields a polynomial algorithm to find such a vertex. Furthermore, as another consequence of our main theorem, we get a result of Alspach (Canad. Math. Bull. 10, 1967, 283–286) that states that every arc of a regular tournament is pancyclic