Edge-disjoint Hamiltonian cycles in hypertournaments

We introduce a method for reducing k-tournament problems, for k >= 3, to ordinary tournaments, that is, 2-tournaments. It is applied to show that a k-tournament on n >= k + 1 + 24d vertices (when k >= 4) or on n >= 30d + 2 vertices (when k = 3) has d edge-disjoint Hamiltonian cycles if and only if it is d-edge-connected. Ironically, this is proved by ordinary tournament arguments although it only holds for k >= 3. We also characterizatize the pancyclic k-tournaments, a problem posed by Gutin and Yeo.(Our characterization is slightly incomplete in that we prove it only for n large compared to k.) (c) 2005 Wiley Periodicals, Inc.