PANCYCLIC ARCS IN HAMILTONIAN CYCLES OF HYPERTOURNAMENTS

A k-hypertournament H on n vertices, where 2 � kn, is a pair H = (V,A), where V is the vertex set of H and A is a set of k-tuples of vertices, called arcs, such that for all subsets SV with |S| = k, A contains exactly one permutation of S as an arc. Recently, Li et al. showed that any strong k-hypertournament H on n vertices, where 3 � kn 2, is vertex-pancyclic, an extension of Moon's theorem for tournaments. In this paper, we prove the following generalization of another of Moon's theorems: If H is a strong k-hypertournament on n vertices, where 3 � kn 2, and C is a Hamiltonian cycle in H, then C contains at least three pancyclic arcs.