2019/09/17 by Yuan Hou, Hou, Yuan, An Chang +3 · 2 citations
Computer Science · Mathematics · #05C35 (Secondary) #05C50 (Primary) 05C65 #Combinatorics (math.CO) #FOS: Mathematics #G.2.2 #Limits and Structures in Graph Theory #Matrix Theory and Algorithms #Tensor decomposition and applications
paper · pdf · doi:10.48550/arxiv.1909.08120
openalex publication_date 2019/09/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 C4-free linear 3-uniform hypergraphs.