Edge intersection graphs of linear 3-uniform hypergraphs

Let L3l be the class of edge intersection graphs of linear 3-uniform hypergraphs. The problem of recognizing G∈L3l is NP-complete. Denote by δALG the minimal integer such that the problem "G∈L3l" 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 L3l 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.