Domination, matching and transversal numbers for Berge-G hypergraphs

Let $G=(V(G),E(G))$ be a graph and $H=(V(H),E(H))$ be a hypergraph. The hypergraph H is a { Berge-G} if there is a bijection f : E(G) ↦ E(H) such that for each e ∈ E(G) we have e ⊆ f(e). We define { dilations of G} as a particular subfamily of not necessarily uniform Berge-G hypergraphs. We examine domination, matching and transversal numbers and some relation between these parameters in that family of hypergraphs. Our work generalizes previous results concerning generalized power hypergraphs.