PANCYCLIC ARCS IN HAMILTONIAN CYCLES OF HYPERTOURNAMENTS
Yubao Guo, Michel Surmacs · Journal of the Korean Mathematical Society · 2014
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.