Linear Time Algorithms or Hamiltonian Problems on (Claw, Net)-Free Graphs

Abstract

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.

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Cite this paper

@inproceedings{Brandstdt2016LinearTA, title={Linear Time Algorithms or Hamiltonian Problems on (Claw, Net)-Free Graphs}, author={Andreas Brandst{\"a}dt and Feodor F. Dragan and Ekkehard K{\"{o}hler}, year={2016} }