Spectral radius and Hamiltonicity of uniform hypergraphs

2025/04/25 by Brooks, George, Linz, William, Luo, Ruth
#Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.2504.18314

Abstract

Let n and r be integers with n-2≥ r≥ 3. We prove that any r-uniform hypergraph H on n vertices with spectral radius λ(H) > \binomn-2r-1 must contain a Hamiltonian Berge cycle unless H is the complete graph K_n-1^r with one additional edge. This generalizes a result proved by Fiedler and Nikiforov for graphs. As part of our proof, we show that if |H| > \binomn-1r, then H contains a Hamiltonian Berge cycle unless H is the complete graph K_n-1^r with one additional edge, generalizing a classical theorem for graphs.

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