Spectral radius and Hamiltonicity of uniform hypergraphs

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 ) > ( n − 2 r − 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 | > ( n − 1 r ) , 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.