Whist tournaments with the three person property

Authors:
Gennian Ge;C. W. H. Lam
Affiliations:
Department of Mathematics, Zhejiang University, Hangzhou 310027, Zhejiang, People's Republic of China;Department of Computer Science, Concordia University, Montreal, Québec, Canada H3G 1M8
Venue:
Discrete Applied Mathematics
Year:
2004

Citing 4
Cited 4

Design theory

Design theory
Whist tournaments—three person property

Discrete Applied Mathematics
The spectrum of HSOLSSOM(hn) where h is even

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Existence of whist tournaments with the three-person property 3PWh(v)

Discrete Applied Mathematics

Existence of directedwhist tournaments with the three person property 3PDWh(v)

Discrete Applied Mathematics
Existence of Z-cyclic 3PDTWh(p) for Prime p ≡ 1 (mod 4)

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Triplewhist tournaments with the three person property

Journal of Combinatorial Theory Series A
Existence of directed triplewhist tournaments with the three person property 3PDTWh(v)

Discrete Applied Mathematics

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Abstract

A whist tournament Wh(υ) is said to have the three person property if any two games in the tournament do not have three common players. We denote such a design as 3PWh(υ). It is proved in the literature that a 3PWh(υ) exists for any υ ≥ 8 and υ ≡ 0, 1 mod 4 with 38 possible exceptions. In this paper, we resolve these open cases and complete the spectrum problem on the existence of 3PWh(υ)s.