Degree conditions restricted to induced paths for hamiltonicity of claw-heavy graphs

Broersma and Veldman proved that every 2-connected claw-free and P ₆-free graph is hamiltonian. Chen et al. extended this result by proving every 2-connected claw-heavy and P ₆-free graph is hamiltonian. On the other hand, Li et al. constructed a class of 2-connected graphs which are claw-heavy and P ₆-o-heavy but not hamiltonian. In this paper, we further give some Ore-type degree conditions restricting to induced copies of P ₆ of a 2-connected claw-heavy graph that can guarantee the graph to be hamiltonian. This improves some previous related results.