@article{19ccf5a39608414e8f7c7ae787abae70,

title = "Dominating sets in k-majority tournaments",

abstract = "A k-majority tournament T on a finite vertex set V is defined by a set of 2 k - 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 k log k for suitable positive constants C1 and C2.",

keywords = "Dominating set, Tournament, k-majority",

author = "Noga Alon and Graham Brightwell and Kierstead, {H. A.} and Kostochka, {A. V.} and Peter Winkler",

note = "Funding Information: Kierstead), kostochk@math.uiuc.edu (A.V. Kostochka), peter.winkler@dartmouth.edu (P. Winkler). 1Research supported in part by a USA-Israeli BSF grant, by the Israel Science Foundation and by the Hermann Minkowski Minerva Center for Geometry at Tel Aviv University. 2Supported in part by NSA Grant MDA904-03-1-0007. 3Supported in part by NSF Grants DMS-0099608 and DMS-0400498. 4Work done while at Bell Labs, Lucent Technologies and at Institute for Advanced Study, supported in part by NMIMT/ICASA grant MDA904-01-C-0327.",

year = "2006",

month = may,

doi = "10.1016/j.jctb.2005.09.003",

language = "אנגלית",

volume = "96",

pages = "374--387",

journal = "Journal of Combinatorial Theory. Series B",

issn = "0095-8956",

publisher = "Academic Press Inc.",

number = "3",

}