Triplewhist tournaments with the three person property

Abstract: The necessary conditions for existence of a triplewhist tournament are . By the efforts of many authors through a century, these conditions are shown to be sufficient except for and possibly for . A triplewhist tournament 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 . In this paper, we extend the known existence result for s and show that the necessary conditions for existence of a , namely, and , are also sufficient except for and possibly for . [Copyright &y& Elsevier]