Spectral extremal results for hypergraphs (Q2049621)

Summary: 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 \(\mathcal{F}\), we say that a hypergraph \(H\) is Berge \(\mathcal{F}\)-free if for every \(F \in \mathcal{F}\), 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.