### Abstract

A k-majority tournament T on a finite vertex set V is defined by a set of 2 k - 1 linear orderings of V, with u → v if and only if u lies above v in at least k of the orders. Motivated in part by the phenomenon of "non-transitive dice", we let F ( k ) be the maximum over all k-majority tournaments T of the size of a minimum dominating set of T. We show that F ( k ) exists for all k > 0, that F ( 2 ) = 3 and that in general C_{1} k / log k ≤ F ( k ) ≤ C_{2} k log k for suitable positive constants C_{1} and C_{2}.

Original language | English (US) |
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Pages (from-to) | 374-387 |

Number of pages | 14 |

Journal | Journal of Combinatorial Theory. Series B |

Volume | 96 |

Issue number | 3 |

DOIs | |

State | Published - May 2006 |

### Keywords

- Dominating set
- Tournament
- k-majority

### ASJC Scopus subject areas

- Theoretical Computer Science
- Discrete Mathematics and Combinatorics
- Computational Theory and Mathematics

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## Cite this

Alon, N., Brightwell, G., Kierstead, H., Kostochka, A. V., & Winkler, P. (2006). Dominating sets in k-majority tournaments.

*Journal of Combinatorial Theory. Series B*,*96*(3), 374-387. https://doi.org/10.1016/j.jctb.2005.09.003