We consider round-robin sports tournaments with $n$ teams and $n-1$ rounds. We construct an infinite family of opponent schedules for which every home-away assignment induces at least $n(n-2)/4$ breaks. This construction establishes a matching lower bound for a corresponding upper bound from the literature.
- break minimization
- Sports scheduling
- sports tournament
- Latin squares
Brouwer, A. E., Post, G. F., & Woeginger, G. (2008). Tight bounds for break minimization in tournament scheduling. Journal of combinatorial theory. Series A, 115(Supplement/6), 1065-1068. https://doi.org/10.1016/j.jcta.2007.10.002