EDGE INTERSECTION HYPERGRAPHS.

If H = (V, ε) is a hypergraph, its edge intersection hypergraph EI(H) = (V, εEI) has the edge set εEI = {e1 ∩ e2 | e1, e2 ∈ ε ∧ e1 ≠ e2 ∧ |e1 ∩ e2| ≥ 2}. Besides investigating several structural properties of edge intersection hypergraphs, we prove that all trees but seven exceptional ones are edge intersection hypergraphs of 3-uniform hypergraphs. Using the so-called clique-fusion, as a conclusion we obtain that nearly all cacti are edge intersection hypergraphs of 3-uniform hypergraphs, too. [ABSTRACT FROM AUTHOR]