Triplewhist tournaments with the three person property

Authors:
Gennian Ge
Affiliations:
Department of Mathematics, Zhejiang University, Hangzhou 310027, Zhejiang, PR China
Venue:
Journal of Combinatorial Theory Series A
Year:
2007

Citing 10
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Whist tournaments with the three person property

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Some difference matrix constructions and an almost completion for the existence of triplewhist tournaments TWh(v)

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Existence of Z-cyclic 3PTWh (p) for any Prime p≡ 1 (mod 4)

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Handbook of Combinatorial Designs, Second Edition (Discrete Mathematics and Its Applications)

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

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Existence of directed triplewhist tournaments with the three person property 3PDTWh(v)

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Abstract

The necessary conditions for existence of a triplewhist tournament TWh(v) are v=0,1(mod4). By the efforts of many authors through a century, these conditions are shown to be sufficient except for v=5,9,12,13 and possibly for v=17. A triplewhist tournament Wh(v) is said to have the three person property if any two games in the tournament do not have three common players. We briefly denote such a design as a 3PTWh(v). In this paper, we extend the known existence result for TWh(v)s and show that the necessary conditions for existence of a 3PTWh(v), namely, v=8 and v=0,1(mod4), are also sufficient except for v=9,12,13 and possibly for v=17.