|
|||||
|
|
The existence and uniqueness of strong kings in tournaments |
|
| Authors: | An-Hang Chen Yuwen Cheng |
| Institution: | a Department of Information Management, National Taiwan University of Science and Technology, Taipei, Taiwan, ROC b Department of Information Management, National Taipei College of Business, Taipei, Taiwan, ROC c Department of Mathematics, National Taitung University, Taitung, Taiwan, ROC d Department of Computer Science and Information Engineering, National Chi Nan University, Nantou, Taiwan, ROC |
| Abstract: | A king x in a tournament T is a player who beats any other player y directly (i.e., x→y) or indirectly through a third player z (i.e., x→z and z→y). For x,y∈V(T), let b(x,y) denote the number of third players through which x beats y indirectly. Then, a king x is strong if the following condition is fulfilled: b(x,y)>b(y,x) whenever y→x. In this paper, a result shows that for a tournament on n players there exist exactly k strong kings, 1?k?n, with the following exceptions: k=n-1 when n is odd and k=n when n is even. Moreover, we completely determine the uniqueness of tournaments. |
| Keywords: | Tournaments Kings Strong kings Score sequences |
| 本文献已被 ScienceDirect 等数据库收录！ | |