### 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 |
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Place of Publication | Enschede |

Publisher | University of Twente |

Number of pages | 14 |

ISBN (Print) | 0169-2690 |

Publication status | Published - 2005 |

### Publication series

Name | Memorandum Afdeling TW |
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Publisher | Department of Applied Mathematics, University of Twente |

No. | 1760 |

ISSN (Print) | 0169-2690 |

### Keywords

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

## Cite this

Post, G. F., & Woeginger, G. (2005).

*Sports tournaments, home-away assignments, and the break minimization problem*. (Memorandum Afdeling TW; No. 1760). Enschede: University of Twente.