A characterization of graphical covers (Q1082354)

In a short paper the two authors consider a family \({\mathcal S}\) of sets, define a graph G(\({\mathcal S})\) in the following natural way: The set of vertices of G(\({\mathcal S})\) is \(X=\cup {\mathcal S}\) and the set of edges consists of all unordered pairs of distinct vertices for which there exists a member of \({\mathcal S}\) to which both belong. Then they introduce the concept 'The family of \({\mathcal S}\) is graphical' or '\({\mathcal S}\) is a graphical cover of X' and finally they give some characterizations of graphical covers.