Hypergraphs with large domination number and with edge sizes at least three

Let H=(V,E)H=(V,E) be a hypergraph with vertex set VV and edge set EE. A dominating set in HH is a subset of vertices D⊆VD⊆V such that for every vertex v∈V∖Dv∈V∖D there exists an edge e∈Ee∈E for which v∈ev∈e and e∩D≠0̸e∩D≠0̸. The domination number γ(H)γ(H) is the minimum cardinality of a dominating set in HH. It is known that if HH is a hypergraph of order nn with edge sizes at least three and with no isolated vertex, then γ(H)≤n/3γ(H)≤n/3. In this paper, we characterize the hypergraphs achieving equality in this bound.