The number of kings in a multipartite tournament Original Research Article

We show that in any n-partite tournament, where n ⩾ 3, with no transmitters and no 3-kings, the number of 4-kings is at least eight. All n-partite tournaments, where n ⩾ 3, having eight 4-kings and no 3-kings are completely characterized. This solves the problem proposed in Koh and Tan (accepted).