  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
$P_6$-\emph{o}-heavy but not hamiltonian. In this paper we further give some
Ore-type degree conditions restricting to induced $P_6$'s of a 2-connected
claw-heavy graph that can guarantee the graph to be hamiltonian. This improves
some previous related results.
