A k -hypertournament H on n vertices with 2 ź k ź n is a pair H = ( V , A H ) , where V is a set of n vertices and A H is a set of k -tuples of vertices, called arcs, such that for any k -subset S of V , A H contains exactly one of the k ! k -tuples whose entries belong to S . Obviously, a 2 -hypertournament is a tournament.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 ź k ź n - 2 , there is a Hamiltonian cycle C containing at least three pancyclic arcs, each of which belongs to an m -cycle C m for each m ź { 3 , 4 , ź , n } such that V ( C 3 ) ź V ( C 4 ) ź ź ź V ( C n ) .
['Hongwei Li', 'Wenjie Ning', 'Yubao Guo', 'Mei Lu']
On pancyclic arcs in hypertournaments