The Spectral Radii of Intersecting Uniform Hypergraphs

Peng-Li Zhang, Xiao-Dong Zhang
2020 Communications on Applied Mathematics and Computation  
The celebrated Erdős-Ko-Rado theorem states that given n ⩾ 2k, every intersecting k-uniform hypergraph G on n vertices has at most n − 1 k − 1 edges. This paper states spectral versions of the Erdős-Ko-Rado theorem: let G be an intersecting k-uniform hypergraph on n vertices with n ⩾ 2k. Then, the sharp upper bounds for the spectral radius of A (G) and is a convex linear combination of the degree diagonal tensor D(G) and the adjacency tensor A(G) for 0 ⩽ < 1, and Q * (G) is the incidence
more » ... r, respectively. Furthermore, when n > 2k, the extremal hypergraphs which attain the sharp upper bounds are characterized. The proof mainly relies on the Perron-Frobenius theorem for nonnegative tensor and the property of the maximizing connected hypergraphs.
doi:10.1007/s42967-020-00073-7 fatcat:qizeyvoywvazpm7wzvrgqlflva