A complete solution of a problem of Bondy concerning multipartite tournaments (Q1907115)

An \(n\)-partite tournament is an orientation of a complete \(n\)-partite graph. In 1976, Bondy raised the following problem: does every strong \(n\)-partite \((n \geq 5)\) tournament, with at least two vertices in each partite set, contain an \((n + 1)\)-cycle? A negative answer to this question was obtained by the reviewer in 1982 and, independently, by R. Balakrishnan and P. Paulraja in 1984. The purpose of this paper is to provide a characterization of all such \(n\)-partite tournaments without \((n + 1)\)-cycles.