Journal of the
Korean Mathematical Society JKMS

A $k$-hypertournament $H$ on $n$ vertices, where $2\leq k\leq n$, 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 $S\subseteq V$ 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 $3\leq k\leq n-2$, 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 $3\leq k\leq n-2$, and $C$ is a Hamiltonian cycle in $H$, then $C$ contains at least three pancyclic arcs.

Keywords: tournament, hypertournament, semicomplete digraph, pancyclic arc, Hamiltonian cycle

MSC numbers: 05C65, 05C20