The H H -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 H H -force set) of G G if every X X -cycle of G G (i.e.,a cycle of G G containing all vertices of X X ) is hamiltonian. For the graph G G , h(G) h ( G ) is the smallest cardinality of an H H -force set of G G and call it the H H -force number of G G . In this paper, the definitions of the H H -force set and the H H -force number are extended on hypertournaments by using cycles of hypertournaments instead of the cycles of undirected graphs and, the smallest possible H H -force set of a k k -hypertournament with n?k+3 n ? k + 3 vertices is characterized and its H H -force number is given unless it belongs to the exceptional classes of k k -hypertournaments.
hypertournaments h h -force set h h h h h h h -force number h h h h h