The structure of strong tournaments containing exactly one out-arc pancyclic vertex

An arc in a tournament T with n ≥ 3 vertices is called pancyclic if it belongs to a cycle of length l for all 3 ≤ l ≤ n. We call a vertex u of T an out-arc pancyclic vertex of T if each out-arc of u is pancyclic in T . Yao, Guo and Zhang [Discrete Appl. Math. 99 (2000), 245–249] proved that every strong tournament contains at least one out-arc pancyclic vertex, and they gave an infinite class of strong tournaments, each of which contains exactly one out-arc pancyclic vertex. In this paper we give the structure of strong tournaments containing exactly one out-arc pancyclic vertex.