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Hamiltonicity in Partly claw-free graphs

Published online by Cambridge University Press:  28 January 2009

Moncef Abbas  and
Zineb Benmeziane
Moncef Abbas
Affiliation:
Université des Sciences et de la Technologie Houari Boumedienne Faculté de Mathématiques, BP 32, El Alia Alger 16111, Algérie; zbenmeziane@yahoo.fr
Zineb Benmeziane
Affiliation:
Université des Sciences et de la Technologie Houari Boumedienne Faculté de Mathématiques, BP 32, El Alia Alger 16111, Algérie; zbenmeziane@yahoo.fr
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Abstract


Matthews and Sumner have proved in [10] that if G is a 2-connected claw-free graph of order n such that δ(G) ≥ (n-2)/3, then G is Hamiltonian. We say that a graph is almost claw-free if for every vertex v of G, 〈N(v)〉 is 2-dominated and the set A of centers of claws of G is an independent set. Broersma et al. [5] have proved that if G is a 2-connected almost claw-free graph of order n such that n such that δ(G) ≥ (n-2)/3, then G is Hamiltonian. We generalize these results by considering the graphs satisfying the following property: for every vertex v ∈ A, there exist exactly two vertices x and y of V\A such that N(v) ⊆ N[x] ∪ N[y]. We extend some other known results on claw-free graphs to this new class of graphs.

Keywords

Graph theoryclaw-free graphsalmost claw-free graphsHamiltonicitymatching.
Type
Research Article
Information
RAIRO - Operations Research , Volume 43 , Issue 1 , January 2009 , pp. 103 - 113
Copyright
© EDP Sciences, ROADEF, SMAI, 2009

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