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Ordered tournaments and ordered triplewhist tournaments with the three person property

✍ Scribed by R. J. R. Abel; Gennian Ge

Publisher
John Wiley and Sons
Year
2009
Tongue
English
Weight
153 KB
Volume
17
Category
Article
ISSN
1063-8539

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✦ Synopsis

Abstract

It is well known that an ordered tournament OWh(v) exists if and only if v ≑ 1 (mod 4), v β‰₯ 5. An ordered triplewhist tournament on v players is said to have the three person property if no two games in the tournament have three common players. We briefly denote such a design as a 3POTWh(v). In this article, we show that a 3POTWh(v) exists whenever v>17 and v ≑ 1 (mod 4) with few possible exceptions. We also show that an ordered whist tournament on v players with the three person property, denoted 3POWh(v), exists if and only if v ≑ 1 (mod 4), v β‰₯ 9. Β© 2008 Wiley Periodicals, Inc. J Combin Designs 17: 39–52, 2009

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The dichromatic number k(D) of a digraph D is the minimum number of acyclic sets in which V(D) can be partitioned. If de(D) = Y, D is said r-dichromatic. In this paper it is proved that the minimum order of a 3-dichromatic (resp. 4-dichromatic) tournament is 7 (resp. 11). It is also proved that ther