Spectral bipartite Turan problems on linear hypergraphs

Let F be a graph and let Bᵣ(F) be the class of r-uniform Berge-F hypergraphs. In this paper, by establishing a relationship between the spectral radius of the adjacency tensor of a uniform hypergraph and its local structure via walks, we give a spectral asymptotic bound for Bᵣ(C₃)-free linear r-uniform hypergraphs and upper bounds for the spectral radii of Bᵣ(K2,t)-free or ᵣ(Ks,t),Bᵣ(C₃)\-free linear r-uniform hypergraphs, where C₃ and Ks,t are respectively the triangle and the complete bipartite graph with one part having s vertices and the other part having t vertices. Our work implies an upper bound for the number of edges of ᵣ(Ks,t),Bᵣ(C₃)\-free linear r-uniform hypergraphs, and extends some known work on (spectral) extreme problems of hypergraphs.