Edge intersection graphs of linear 3-uniform hypergraphs

Let be the class of edge intersection graphs of linear 3-uniform hypergraphs. It is known that the problem of recognition of the class is NP-complete. We prove that this problem is polynomially solvable in the class of graphs with minimum vertex degree ≥10. It is also proved that the class is characterized by a finite list of forbidden induced subgraphs in the class of graphs with minimum vertex degree ≥16.