The HH-force set of a hypertournament

Let G=(V,E)G=(V,E) be a hamiltonian undirected graph. A nonempty vertex set X⊆V(G)X⊆V(G) is called a hamiltonian cycle enforcing set (in short, an HH-force set) of GG if every XX-cycle of GG (i.e., a cycle of GG containing all vertices of XX) is hamiltonian. For the graph GG, h(G)h(G) is the smallest cardinality of an HH-force set of GG and call it the HH-force number of GG. In this paper, the definitions of the HH-force set and the HH-force number are extended on hypertournaments by using cycles of hypertournaments instead of the cycles of undirected graphs and, the smallest possible HH-force set of a kk-hypertournament with n≥k+3n≥k+3 vertices is characterized and its HH-force number is given unless it belongs to the exceptional classes of kk-hypertournaments.