A -hypertournament on vertices, where , is a pair , where is the vertex set of and is a set of -tuples of vertices, called arcs, such that, for all subsets with , contains exactly one permutation of as an arc. Gutin and Yeo (1997) showed in [2] that any strong -hypertournament on vertices, where , is Hamiltonian, and posed the question as to whether the result could be extended to vertex-pancyclicity. As a response, Petrovic and Thomassen (2006) in [4] and Yang (2009) in [6] gave some sufficient conditions for a strong hypertournament to be vertex-pancyclic.
In this paper, we prove that, if is a strong -hypertournament on vertices, where , then is vertex-pancyclic. This extends the aforementioned results and Moon’s theorem for tournaments. Furthermore, our result is best possible in the sense that the bound is tight.