A short proof of a theorem on Hamiltonian graphs

In this note, we give a short proof of a stronger version of the following theorem: Let G be a 2-connected graph of order n such that \documentclass{article}\pagestyle{empty}\begin{document}$ d(u)+d(v)+d(w) \geq n + \mid N(u) \cap N(v) \cap N(w) \mid $\end{document} for any independent set {u, v, w}, then G is hamiltonian. © 1996 John Wiley & Sons Inc.