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Spectral radius and Hamiltonicity of graphs with large minimum degree

Vladimir Nikiforov — 2016

Czechoslovak Mathematical Journal

Let G be a graph of order n and λ ( G ) the spectral radius of its adjacency matrix. We extend some recent results on sufficient conditions for Hamiltonian paths and cycles in G . One of the main results of the paper is the following theorem: Let k ≥ 2 , n ≥ k 3 + k + 4 , and let G be a graph of order n , with minimum degree δ ( G ) ≥ k . If λ ( G ) ≥ n - k - 1 , then G has a Hamiltonian cycle, unless G = K 1 ∨ ( K n - k - 1 + K k ) or G = K k ∨ ( K n - 2 k + K ¯ k ) .

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