The number of vertices whose out-arcs are pancyclic in a 2-strong tournament

An arc going out from a vertex x in a digraph is called an out-arc of x. Yao et al. [Discrete Appl. Math. 99 (2000) 245–249] proved that every strong tournament contains a vertex x such that all out-arcs of x are pancyclic. Recently, Yeo [J. Graph Theory 50 (2005) 212–219] proved that each 3-strong tournament contains two such vertices. In this paper, we confirm that Yeo's result is also true for 2-strong tournaments. Our proof implies a polynomial algorithm to find two such vertices.