Dominating sets in k-majority tournaments

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

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

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.

Original languageEnglish
Pages (from-to)374-387
Number of pages14
JournalJournal of Combinatorial Theory. Series B
Volume96
Issue number3
DOIs
StatePublished - May 2006

Funding

FundersFunder number
Hermann Minkowski Minerva Center for Geometry
NMIMT/ICASAMDA904-01-C-0327
USA-Israeli BSF
National Science FoundationDMS-0400498, DMS-0099608
Directorate for Mathematical and Physical Sciences0400498, 0099608
National Sanitarium AssociationMDA904-03-1-0007
Israel Science Foundation
Tel Aviv University

    Keywords

    • Dominating set
    • Tournament
    • k-majority

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