When n-cycles in n-partite tournaments are longest cycles

An n-tournament is an orientation of a complete n-partite graph. It was proved by J.A. Bondy in 1976 that every strong n-partite tournament has an n-cycle. We characterize strong n-partite tournaments in which a longest cycle is of length n and, thus, settle a problem in Volkmann (Discrete Math. 199 (1999) 279).