A local tournament contains a vertex whose out-arcs are pseudo-girth-pancyclic

An arc leaving a vertex x in a digraph is called an out‐arc of x. Thomassen (J Combin Theory Ser B 28 (1980), 142–163) proved that every strong tournament contains a vertex whose every out‐arc is contained in a Hamiltonian cycle. In 2000, Yao et al. (Discrete Appl Math 99 (2000), 245–249) improved the result of Thomassen and confirmed that every strong tournament contains a vertex whose out‐arcs are pancyclic. In this article, we extend the result of Yao et al. to local tournaments and obtain a best possible result in some sense. © 2009 Wiley Periodicals, Inc. J Graph Theory 62: 346–361, 2009