Edge intersection graphs of linear 3-uniform hypergraphs

Let L3 be the class of edge intersection graphs of linear 3-uniform hypergraphs. The problem of recognizing G ∈ L3 is NP-complete. Denote by δALG the minimal integer such that the problem ”G ∈ L3 ” is polynomially solvable in the class of graphs G with the minimal vertex degree δ(G) ≥ δALG and by δFIS the minimal integer such that L3 can be characterized by a finite list of forbidden induced subgraphs in the class of graphs G with δ(G) ≥ δFIS . It is proved that δALG ≤ 10 and δFIS ≤ 16.