In our earlier papers, we studied the mathematical structure of equitable round-robin tournaments with home-away assignments. Using some necessary conditions for their feasibility in terms of (cyclic) break interval sequences, we enumerated all the feasible home-away tables of such tournaments with maximal break interval greater than or equal to 4 (resp. 5), up to 26 teams (resp. 42 teams).

In this paper, we investigate how the maximal value of the maximal break intervals for feasible and equitable round-robin tournaments grows when the number of teams increases. In particular, we see that the maximal value of the maximal break intervals increases by 1 when the number of teams reaches a power of 2, by computational experiments. Further, we give a general method to construct a schedule of 4n teams with maximal break interval  from a schedule of 2n teams with maximal break interval k.

Based on computational results, we prove some theorems about the behavior of the maximal value of the maximal break intervals for feasible and equitable round-robin tournaments with 2n teams.

sports scheduling, equitable round-robin tournament, home-away table, friend-enemy table, break interval sequence, maximal break interval.