The minimum number of vertices in uniform hypergraphs with given domination number

Csilla Bujtás, Balázs Patkós, Z. Tuza, Máté Vizer

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

The . domination number . γ(H) of a hypergraph . H=(V(H),E(H)) is the minimum size of a subset . D⊂V(H) of the vertices such that for every . v∈V(H)(set minus)D there exist a vertex . d∈D and an edge . H∈E(H) with . v,d∈H. We address the problem of finding the minimum number . n(k,γ) of vertices that a . k-uniform hypergraph . H can have if . γ(H)≥γ and . H does not contain isolated vertices. We prove that . n(k,γ)=k+Θ(k1-1/γ)and also consider the . s-wise dominating and the distance-l dominating version of the problem. In particular, we show that the minimum number . ndc(k,γ,l) of vertices that a connected . k-uniform hypergraph with distance-l domination number . γ can have isroughly . kγl2.

Original languageEnglish
JournalDiscrete Mathematics
DOIs
Publication statusAccepted/In press - Mar 29 2016

Keywords

  • Distance domination
  • Domination number
  • Extremal problem
  • Hypergraph
  • Multiple domination

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics

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