Note on set representation of bounded degree hypergaphs

In their classical paper, Erdős, Goodman and Pósa studied the representation of a graph with vertex set $[n]$ by a family of subsets $S_1,\dots ,S_n$ with the property that $\{i,j\}$ is an edge if and only if $S_i\cap S_j\mathrm{\ne }\mathrm{\varnothing }$. In this note, we consider a similar representation of bounded degree $r$-uniform hypergraphs and establish some bounds for a corresponding problem.