Degree Sums, kappa-Factors and Hamiltonian Cycles in Graphs

摘要

The authors prove (a generalization of) the following conjecture of R. Haggkvist: Let G be a 2-connected graph on n vertices where every pair of nonadjacent vertices has degree sum at least n - k and assume that G has a k-factor; then G is hamiltonian. This result is a common generalization of well-known theorems of Ore and Jackson, respectively.