Triplewhist tournaments with the three person property

摘要

The necessary conditions for existence of a triplewhist tournament TWh(v) are v equivalent to 0, 1 (mod 4). 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 equivalent to 0, 1 (mod 4), are also sufficient except for v = 9, 12, 13 and possibly for v = 17. (c) 2007 Elsevier Inc. All rights reserved.