Edge-disjoint Hamiltonian cycles in hypertournaments

Abstract

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.) © 2005 Wiley Periodicals, Inc.