Spectral Extremal Results for Hypergraphs - Hou, Yuan; Chang, An; Cooper, Joshua (The Electronic Journal of Combinatorics, 2021)
Let F be a graph. A hypergraph is called Berge F if it can be obtained by replacing each edge in F by a hyperedge containing it. Given a family of graphs F, we say that a hypergraph H is Berge F-free if for every F F, the hypergraph H does not contain a Berge F as a subhypergraph. In this paper we investigate the connections between spectral radius of the adjacency tensor and structural properties of a linear hypergraph. In particular, we obtain a spectral version of Turán-type problems over linear k-uniform hypergraphs by using spectral methods, including a tight result on Berge C_4-free linear 3-uniform hypergraphs.