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An algorithm for constructing edge-trees from hypergraphs

Consider a hypergraph H = (E, P) where E denotes the set of vertices and P the set of edges. The hypergraph H = (E, P) is called an edge-tree hypergraph if there exists a tree T with edge set E such that every p = P is a path in T. We describe a polynomial time algorithm for deciding whether a given hypergraph H = (E, P) is an edge-tree hypergraph. The algorithm can be used to decide whether a binary matroid is graphic or not.