๐”– Bobbio Scriptorium
โœฆ   LIBER   โœฆ

On the existence of kings in continuous tournaments

โœ Scribed by Masato Nagao; Dmitri Shakhmatov


Book ID
116920771
Publisher
Elsevier Science
Year
2012
Tongue
English
Weight
181 KB
Volume
159
Category
Article
ISSN
0166-8641

No coin nor oath required. For personal study only.


๐Ÿ“œ SIMILAR VOLUMES


On the existence of triplewhist tourname
โœ Y. Lu; L. Zhu ๐Ÿ“‚ Article ๐Ÿ“… 1997 ๐Ÿ› John Wiley and Sons ๐ŸŒ English โš– 141 KB ๐Ÿ‘ 2 views

It is well known that a triplewhist tournament TWh(v) exists only if v โ‰ก 0 or 1 (mod 4) and v = 5, 9. In this article, we introduce a new concept TWh-frame and use it to show that the necessary condition for the existence of a TWh(v) is also sufficient with a handful possible exceptions of v โˆˆ {12,

On the existence of specified cycles in
โœ Abdelhamid Benhocine; A. Pawel Wojda ๐Ÿ“‚ Article ๐Ÿ“… 1983 ๐Ÿ› John Wiley and Sons ๐ŸŒ English โš– 241 KB ๐Ÿ‘ 1 views

For 2 s p s n and n 2 3, D(n, p) denotes the digraph with n vertices obtained from a directed cycle of length n by changing the orientation of p -1 consecutives edges. In this paper, we prove that every tournament of order n 2 7 contains D(n, p ) for p = 2, 3, ..., n. Furthermore, we determine the t

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.

The number of kings in a multipartite to
โœ K.M. Koh; B.P. Tan ๐Ÿ“‚ Article ๐Ÿ“… 1997 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 401 KB

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).