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.Full text not available from this repository.
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)|
|Additional Information:||© 2004 the authors|
|Library of Congress subject classification:||Q Science > QA Mathematics|
|Sets:||Departments > Mathematics|
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