Forbidden Subgraphs, Stability and Hamiltonicity

We study the stability of some classes of claw-free graphs defined in terms of forbidden subgraphs under the closure operation defined in [10]. We characterize all connected graphs A such that the class of all CA-free graphs (where C denotes the claw) is stable. Using this result, we prove that every 2-connected and CHP 8 -free, CHZ 5 -free or CHN 1;1;4 -free graph is either hamiltonian or belongs to some classes of exceptional graphs (all of them having connectivity 2)