Some new triplewhist tournaments TWh(v)

Authors:
G. Ge;C. W. H. Lam
Affiliations:
Department of Mathematics, Suzhou University, Suzhou, 215006, People's Republic of China;Department of Computer Science, Concordia University, 1455 de Maisonneuve Blvd, Montreal, Que., H3G 1M8, Canada
Venue:
Journal of Combinatorial Theory Series A
Year:
2003

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Abstract

It was Moore who first introduced the triplewhist tournament TWh(υ) problem in 1896. It is proved in the literature that the necessary condition for the existence of a TWh(υ), namely, υ ≡ 0 or 1 (mod4), is also sufficient except for υ ≡ 5,9 and possibly excepting υ ∈ {12, 56} ∪ {13, 17, 45, 57, 65, 69, 77, 85, 93,117, 129, 153}. In this paper, it is shown that ther is no TWh(12) and that there does exist a Z-cyclic TWh(υ) for each υ ∈ {44, 45, 48, 52, 56}. This completes the even case for the existence of TWh(υ). By applying frame constructions and product constructions, several new infinite classes of Z-cyclic triplewhist tournaments are then obtained.