Scheduling sports competitions with a given distribution of times (Q1110455)

In some sports competitions there is only one facility (court, etc.) and so teams or individuals are required to play at different times of day. It is desirable that these times of play be equitably distributed for each team, consistent with the constraints imposed by some constants being unable to play at certain times for occupational reasons. This condition, treated as an additional requirement to those of a round-robin tournament, is formulated as a combinatorial design problem and certain cases are solved. In the absence of constraints imposed by particular teams, the problem is that of a balanced tournament design (BTD) and we present a new construction for BTDs with certain parameter values.