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Dominating sets in k-majority tournaments

By Noga Alon, Graham Brightwell, H. A. Kierstead, A. V. Kostochka and Peter Winkler


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

Topics: QA Mathematics
Publisher: Centre for Discrete and Applicable Mathematics, London School of Economics and Political Science
Year: 2004
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Provided by: LSE Research Online
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