A stability result for Berge-K3,t r-graphs and its applications
Abstract
An r-uniform hypergraph (r-graph) is linear if any two edges intersect at most one vertex. For a graph F, a hypergraph H is Berge-F if there is a bijection φ:E(F)→ E(H) such that e⊂eq φ(e) for all e in E(F). In this paper, a kind of stability result for Berge-K3,t linear r-graphs is established. Based on this stability result, an upper bound for the linear Tur\'an number of Berge-K3,t is determined. For an r-graph H, let A(H) be the adjacency tensor of H. The spectral radius of H is the spectral radius of the tensor A(H). Some bounds for the maximum spectral radius of connected Berge-K3,t-free linear r-graphs are obtained.
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