A short proof of a theorem concerning degree sums and connectivity on Hamiltonian graphs

D. Bauer, H. J. Broersma, R. Li, and H. J. Veldman proved that if G is a 2- con nected graph with n vertices such that d(u) + d(v) + d(w) greater than or equal to n + kappa holds for any triple of independent vertices u, v, an d iv, then G is hamiltonian, where kappa is the vertex connectivity of G. I n this note, we will give a short proof of the above result. (C) 1999 Acade mic Press.