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+κholds for any triple of independent verticesu,v, andw, thenGis hamiltonian, whereκis the vertex connectivity ofG. In this note, we will give a short proof of the above result.