Geodesic
Edge intersection hypergraphs
Discussiones Mathematicae. Graph Theory, Tome 44 (2024) no. 1, pp. 101-126

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If ℋ=(V, ℰ ) is a hypergraph, its edge intersection hypergraph EI( ℋ )=(V, ℰ^EI ) has the edge set ℰ^EI={e_1 ∩ e_2 | e_1, e_2 ∈ℰ ∧ e_1 ≠ e_2 ∧ |e_1 ∩ e_2 |≥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.
Keywords: edge intersection hypergraph, tree, cactus 
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Sonntag, Martin; Teichert, Hanns-Martin. Edge intersection hypergraphs. Discussiones Mathematicae. Graph Theory, Tome 44 (2024) no. 1, pp. 101-126. http://geodesic.mathdoc.fr/item/DMGT_2024_44_1_a5/