Elsevier

Information Processing Letters

Volume 87, Issue 6, 30 September 2003, Pages 317-320
Information Processing Letters

Sorting a sequence of strong kings in a tournament

https://doi.org/10.1016/S0020-0190(03)00346-6Get rights and content

Abstract

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 u1,u2,…,un such that uiui+1 (ui beats ui+1) and ui is a king in the sub-tournament induced by {ui,ui+1,…,un} 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 vu 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.

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