A king in a tournament is a player who beats any other player directly or indirectly. According to the existence of a king in every tournament, Wu and Sheng [Inform. Process. Lett. 79 (2001) 297-299] recently presented an algorithm for finding a sorted sequence of kings in a tournament of size n, i.e., a sequence of players u(1), u(2),..., u(n) such that u(i) --> u(i)+(1) (u(i) beats u(i+1)) and ui is a king in the sub-tournament induced by {u(i), u(i)+(1),..., u(n)} for each i = 1, 2,..., n - 1. With each pair u, v of players in a tournament, let b(u, v) denote the number of third players used for u to beat v indirectly. Then, a king u is called a strong king if the following condition is fulfilled: if v --> u then b(u, v) > b(v, u). In the sequel, we will show that the algorithm proposed by Wu and Sheng indeed generates a sorted sequence of strong kings, which is more restricted than the previous one. (C) 2003 Elsevier B.V. All rights reserved.
