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The number of kings in a multipartite tournament

โœ Scribed by K.M. Koh; B.P. Tan


Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
401 KB
Volume
167-168
Category
Article
ISSN
0012-365X

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โœฆ Synopsis


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).


๐Ÿ“œ SIMILAR VOLUMES


Kings in multipartite tournaments
โœ K.M. Koh; B.P. Tan ๐Ÿ“‚ Article ๐Ÿ“… 1995 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 584 KB

Let T be an n-partite tournament and let k,(T) denote the number of r-kings of T. Gutin (1986) and Petrovic and Thomassen (1991) proved independently that if T contains at most one transmitter, then k4(T) >i 1, and found infinitely many bipartite tournaments T with at most one transmitter such that

Number of 4-kings in bipartite tournamen
โœ K.M. Koh; B.P. Tan ๐Ÿ“‚ Article ๐Ÿ“… 1996 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 433 KB

We show that in any bipartite tournament with no transmitters and no 3-kings, the number of 4-kings is at least eight. All such bipartite tournaments having exactly eight 4-kings are completely characterized.

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โœ Ting-Yem Ho; Jou-Ming Chang ๐Ÿ“‚ Article ๐Ÿ“… 2003 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 79 KB

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.

Cycles through arcs in multipartite tour
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Volkmann [L. Volkmann, A remark on cycles through an arc in strongly connected multipartite tournaments, Appl. Math. Lett. 20 (2007Lett. 20 ( ) 1148Lett. 20 ( -1150] ] conjectured that a strong c-partite tournament with c โ‰ฅ 3 contains three arcs that belong to a cycle of length m for each m โˆˆ {3, 4,