### 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 language | English |
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Journal | Discrete Mathematics |

DOIs | |

Publication status | Accepted/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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## Cite this

*Discrete Mathematics*. https://doi.org/10.1016/j.disc.2016.07.007