2-factors and hamiltonicity Original Research Article

We prove the following generalization of a result of Faudree and van den Heuvel. Let G be a 2-connected graph with a 2-factor. If d(u) + d(v) ⩾ n − 2 for all pairs of non-adjacent vertices u, v contained in an induced K1,3, in an induced K1,3 + e or as end-vertices in an induced P4, then G is Hamiltonian.