Centre for Discrete and Applicable Mathematics

 CDAM Research Report, LSE-CDAM-2004-11

June 2004

Dominating Sets in k-Majority Tournaments

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 C1 k/log k < F(k) < C2 klog k for suitable positive constants C1 and C2.

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