A criterion for cyclic whist tournaments with the three person property

Abstract

A  whist tournament is said to have the three person property if the intersection of any two tables in the tournament is at most two. If a is a player at a table in a cyclic whist tournament we introduce the concept of a-centered differences and use this concept to develop a necessary and sufficient condition for the three person property. The well-known whist constructions of Baker, Bose and Cameron, Moore, and Watson are analyzed using this condition. The condition is also generalized to resolvable cyclic block designs of block size k.