Alon, Noga and Brightwell, Graham and Kierstead, H. A. and Kostochka, A. V. and Winkler, Peter
(2004)
*Dominating sets in k-majority tournaments.*
CDAM research report series,
LSE-CDAM-2004-11.
Centre for Discrete and Applicable Mathematics, London School of Economics and Political Science, London, UK.

## Abstract

A k-majority tournament T on a finite vertex set V is defined by a set of 2k − 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 C1k/ log k · F(k) · C2k log k for suitable positive constants C1 and C2.

Item Type: | Monograph (Report) |
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Official URL: | http://www.cdam.lse.ac.uk |

Additional Information: | © 2004 the authors |

Subjects: | Q Science > QA Mathematics |

Sets: | Departments > Mathematics |

Date Deposited: | 19 Nov 2008 13:36 |

Last Modified: | 01 Oct 2010 09:05 |

URI: | http://eprints.lse.ac.uk/id/eprint/13351 |

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