A Bound on the Spectral Radius of Hypergraphs with e Edges

2017/05/03 by Bai, Shuliang, Lu, Linyuan · 1 citation
#05C35 #05C50 #05C65 #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.1705.01593

Abstract

For r≥ 3, let f_r\colon [0,∞)→ [1,∞) be the unique analytic function such that f_r(k\choose r)=k-1\choose r-1 for any k≥ r-1. We prove that the spectral radius of an r-uniform hypergraph H with e edges is at most f_r(e). The equality holds if and only if e=k\choose r for some positive integer k and H is the union of a complete r-uniform hypergraph K_k^r and some possible isolated vertices. This result generalizes the classical Stanley's theorem on graphs.

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• Spectral Turán-type problems for the α-spectral radius of hypergraphs with degree stability

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