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doi:10.1016/S0012-365X(97)00056-3 
Copyright © 1998 Published by Elsevier Science B.V.
Contribution
Hamiltonicity in 2-connected graphs with claws
Received 3 January 1994;
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Abstract
Matthews and Sumner have proved in [12] that if G is a 2-connected claw-free graph of order n such that δ 
(n − 2)/3, then G is hamiltonian. Li has shown that the bound for the minimum degree δ can be reduced to n/4 under the additional condition that G is not in Π, where Π is a class of graphs defined in [7]. On the other hand, we say that a graph G is almost claw-free if the centres of induced claws are independent and their neighbourhoods are 2-dominated. Broersma, Ryjá
ek and Schiermeyer have proved that if G is 2-connected almost claw-free graph of order n such that δ
(n − 2)/3, then G is hamiltonian. We generalize these results by considering the graphs whose claw centres are independent. If G is a 2-connected graph of order n and minimum degree δ such that n 
4δ − 3 and if the set of claw centres of G is independent, then we show that either G is hamiltonian or G ε F, where F is a class of graphs defined in the paper. The bound n 4δ − 3 is sharp.
