Note on set representation of bounded degree hypergaphs

In their classical paper, Erd{o}s, Goodman and Posa studied the representation of a graph by vertex set $[n]$ with a family of subsets S₁,, Sₙ with the property that ,j\ is an edge iff Sᵢ∩ Sⱼ≠ ∅. In this note, we consider a similar representation of bounded degree r-uniform hypergraphs and establish some bounds for a corresponding problem.