Scheduling CCRR tournaments

In this paper, we construct CCRRS, complete coupling round robin schedules, for n teams each consisting of two pairs. The motivation for these schedules is a problem in scheduling bridge tournaments. We construct CCRRS ( n ) for n a positive integer, n ⩾ 3 , with the possible exceptions of n ∈ { 54 , 62 } . For n odd, we show that a CCRRS ( n ) can be constructed using a house with a special property. For n even, a CCRRS ( n ) can be constructed from a Howell design, H ( 2 n - 2 , 2 n ) , with a special property called Property P. We use a combination of direct and recursive constructions to construct H ( 2 n - 2 , 2 n ) with Property P. In order to apply our main recursive construction, we need group divisible designs with odd group sizes and odd block sizes. One of our main results is the existence of these group divisible designs.