Out-arc pancyclicity of vertices in tournaments

Yao, Guo and Zhang [T. Yao, Y. Guo, K. Zhang, Pancyclic out-arcs of a vertex in a tournament, Discrete Appl. Math. 99 (2000) 245–249.] proved that every strong tournament contains a vertex uu such that every out-arc of uu is pancyclic. In this paper, we prove that every strong tournament with minimum out-degree at least two contains two such vertices. Yeo [A. Yeo, The number of pancyclic arcs in a kk-strong tournament, J. Graph Theory 50 (2005) 212–219.] conjectured that every 2-strong tournament has three distinct vertices {x,y,z}{x,y,z}, such that every arc out of x,yx,y and zz is pancyclic. In this paper, we also prove that Yeo’s conjecture is true.