Spectral radius and Hamiltonicity of graphs with large minimum degree

Nikiforov, Vladimir

Czechoslovak Mathematical Journal, Tome 66 (2016) no. 3, pp. 925-940.

Résumé

Let $G$ be a graph of order $n$ and $\lambda (G)$ 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: \endgraf Let $k\ge 2,$ $n\ge k^3+k+4,$ and let $G$ be a graph of order $n$, with minimum degree $\delta (G)\ge k.$ If \[ \lambda ( G) \geq n-k-1, \] then $G$ has a Hamiltonian cycle, unless $G=K_1\vee (K_{n-k-1}+K_k)$ or $G=K_k\vee (K_{n-2k}+{\overline{K}}_k).$

Détail

DOI : 10.1007/s10587-016-0301-y

Classification : 05C35, 05C50
Mots-clés : Hamiltonian cycle; Hamiltonian path; minimum degree; spectral radius