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 + 24 d vertices (when k  ≥ 4) or on n  ≥ 30 d  + 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 .). © 2005 Wiley Periodicals, Inc. J Graph Theory