On the existence of triplewhist tournaments TWh(v)

It is well known that a triplewhist tournament TWh(v) exists only if v ≡ 0 or 1 (mod 4) and v ¬ 5, 9. In this article, we introduce a new concept TWh-frame and use it to show that the necessary condition for the existence of a TWh(v) is also sufficient with a handful possible exceptions of v ∞ {12, 56} ∪ {13, 17, 45, 57, 65, 69, 77, 85, 93, 117, 129, 133, 153}. © 1997 John Wiley & Sons, Inc. J Combin Designs 5: 249–256, 1997