Degree sums,k-factors and hamilton cycles in graphs

We prove (a generalization of) the following conjecture of R. Haggkvist: LetG be a 2-connected graph onn vertices where every pair of nonadjacent vertices has degree sum at leastn — k and assume thatG has ak-factor; thenG is hamiltonian. This result is a common generalization of well-known theorems of Ore and Jackson, respectively.