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) 245249.] proved that every strong tournament contains a vertex u u such that every out-arc of u u 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 k k -strong tournament, J. Graph Theory 50 (2005) 212219.] conjectured that every 2-strong tournament has three distinct vertices {x,y,z} { x , y , z } , such that every arc out of x,y x , y and z z is pancyclic. In this paper, we also prove that Yeos conjecture is true.
out-arcs pancyclicity tournaments cycles