Round-robin tournaments generated by the Circle Method have maximum carry-over

Abstract

The Circle Method is widely used in the field of sport scheduling to generate schedules for round-robin tournaments. If in such a tournament, team A played team B in its previous match and is now playing team C, team C is said to receive a carry-over effect from team B. The so-called carry-over effect value is a number that can be associated to each round-robin schedule; it represents a degree of unbalancedness of the schedule with respect to carry-over. Here, we prove that, for an even number of teams, the Circle Method generates a schedule with maximum carry-over effect value, answering an open question.