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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...
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