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Dominating sets in k-majority tournaments

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.

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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
Rights: http://www.lse.ac.uk/library/usingTheLibrary/academicSupport/OA/depositYourResearch.aspx
Identification Number: LSE-CDAM-2004-11
Date Deposited: 19 Nov 2008 13:36
URL: http://eprints.lse.ac.uk/13351/

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