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 ifGis a 2-connected graph withnvertices such thatd(u)+d(v)+d(w)?n+?holds for any triple of independent verticesu,v, andw, thenGis hamiltonian, where?is the vertex connectivity ofG. In this note, we will give a short proof of the above result.

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[2]  Douglas Bauer,et al.  A generalization of a result of Häggkvist and Nicoghossian , 1989, J. Comb. Theory, Ser. B.