A Bound on the Spectral Radius of Hypergraphs with e Edges [article]

Shuliang Bai, Linyuan Lu
<span title="2017-05-03">2017</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
For r≥ 3, let f_r [0,∞)→ [1,∞) be the unique analytic function such that f_r(k r)=k-1 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 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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