Edge intersection graphs of linear 3-uniform hypergraphs

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