Hamiltonicity in Partly claw-free graphs
Matthews and Sumner have proved in [10] that if is a 2-connected claw-free graph of order such that /3, then is Hamiltonian. We say that a graph is almost claw-free if for every vertex of G, 〈 is 2-dominated and the set of centers of claws of is an independent set. Broersma [5] have proved that if is a 2-connected almost claw-free graph of order such that such that /3, then is Hamiltonian. We generalize these results by considering the graphs satisfying the following property: for...