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 d(u) + d(v)+ d(w) greater than or equal to n + \N(u) boolean AND N(v) boolean AND n(w)\ for any independent set {u, v, w}, then G is hamiltonian. (C) 1996 John Wiley & Sons, Inc.