# Sports tournaments, home-away assignments, and the break minimization problem

Gerhard F. Post, Gerhard Woeginger

Research output: Book/ReportReportProfessional

## Abstract

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 $\frac14 n(n-2)$ breaks. Secondly, for infinitely many $n$, we construct opponent schedules for which at least $\frac16 n(n-1)$ 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 $r\ge3$. This is in strong contrast to the case of $r=2$ rounds, which can be scheduled (in polynomial time) without any breaks.
Original language Undefined Enschede University of Twente 14 0169-2690 Published - 2005

### Publication series

Name Memorandum Afdeling TW Department of Applied Mathematics, University of Twente 1760 0169-2690

• MSC-90B35
• METIS-225439
• IR-65944
• EWI-3580