SIAM Journal on Computing
We prove that claw-free graphs, containing an induced dominating path, have a Hamiltonian path, and that 2-connected claw-free graphs, containing an induced doubly dominating cycle or a pair of vertices such that there exist two internally disjoint induced dominating paths connecting them, have a Hamiltonian cycle. As a consequence, we obtain linear time algorithms for both problems if the input is restricted to (claw,net)-free graphs. These graphs enjoy those interesting structural properties.
Brandstädt, Andreas; Dragan, Feodor F.; and Köhler, Ekkehard (2000). Linear Time Algorithms or Hamiltonian Problems on (Claw, Net)-Free Graphs. SIAM Journal on Computing 30(5), 1662-1677. Retrieved from http://digitalcommons.kent.edu/cspubs/4