Dominating sets in k-majority tournaments

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

Research output: Contribution to journalArticle

17 Scopus citations

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

Keywords

  • Dominating set
  • Tournament
  • k-majority

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics
  • Computational Theory and Mathematics

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