On pancyclic arcs in hypertournaments

Moon (1994) proved that for every strong tournament, there is a Hamiltonian cycle which contains at least three pancyclic arcs. In this paper, we will show that for an arbitrary strong k-hypertournament H with n vertices, where 2≤k≤n−2, there is a Hamiltonian cycle C containing at least three pancyclic arcs, each of which belongs to an m-cycle Cm for each m∈{3,4,…,n} such that V(C3)⊂V(C4)⊂⋯⊂V(Cn).