Ordered tournaments and ordered triplewhist tournaments with the three person property |
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| Authors: | R J R Abel Gennian Ge |
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| Institution: | 1. School of Mathematics and Statistics, University of New South Wales, N.S.W. 2052, Australia;2. Department of Mathematics, Zhejiang University, Hangzhou 310027, Zhejiang, P. R. China |
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| Abstract: | It is well known that an ordered tournament OWh(v) exists if and only if v ≡ 1 (mod 4), v ≥ 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 ≥ 9. © 2008 Wiley Periodicals, Inc. J Combin Designs 17: 39–52, 2009 |
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| Keywords: | whist tournament 3POTWh 3POTWh‐frame |
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