We consider the break minimization problem for fixing home-away assignments in round-robin sports tournaments. First, we show that, for an opponent schedule with n teams and n - 1 rounds, there always exists a home-away assignment with at most frac(1, 4) n ( n - 2 ) breaks. Secondly, for infinitely many n, we construct opponent schedules for which at least frac(1, 6) n ( n - 1 ) breaks are necessary. Finally, we prove that break minimization for n teams and a partial opponent schedule with r rounds is an NP-hard problem for r ≥ 3. This is in strong contrast to the case of r = 2 rounds, which can be scheduled (in polynomial time) without any breaks. © 2006 Elsevier Ltd. All rights reserved.
Post, G., & Woeginger, G. J. (2006). Sports tournaments, home-away assignments, and the break minimization problem. Discrete Optimization, 3(2), 165–173. https://doi.org/10.1016/j.disopt.2005.08.009