Geodesic
Complexity of recognizing edge intersection graphsof hypergraphs with bounded above rank and multiplicity
Trudy Instituta matematiki, Tome 24 (2016) no. 2, pp. 98-105

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Let $L^m_k$ denote the class of edge intersection graphs of hypergraphs with rank at most $k$ and multiplicity at most $m.$ It is proved that the problem of recognizing graphs of the class $L^m_k$ is NP-complete for fixed $k \ge 3,$ $m \ge 1.$ 
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Yu. Metelsky; R. Shatsov. Complexity of recognizing edge intersection graphsof hypergraphs with bounded above rank and multiplicity. Trudy Instituta matematiki, Tome 24 (2016) no. 2, pp. 98-105. http://geodesic.mathdoc.fr/item/TIMB_2016_24_2_a9/