Alon, Noga, Brightwell, Graham, Kierstead, H. A., 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) |
---|---|

Official URL: | http://www.cdam.lse.ac.uk |

Additional Information: | © 2004 the authors |

Library of Congress subject classification: | Q Science > QA Mathematics |

Sets: | Departments > Mathematics |

Identification Number: | LSE-CDAM-2004-11 |

Date Deposited: | 19 Nov 2008 13:36 |

URL: | http://eprints.lse.ac.uk/13351/ |

### Actions (login required)

Record administration - authorised staff only |