Hamiltonicity in partly claw-free graphs
RAIRO - Operations Research - Recherche Opérationnelle, Tome 43 (2009) no. 1, pp. 103-113.

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 δ(G)(n-2)/3, then G is hamiltonian. We generalize these results by considering the graphs satisfying the following property: for every vertex vA, there exist exactly two vertices x and y of VA such that N(v)N[x]N[y]. We extend some other known results on claw-free graphs to this new class of graphs.

DOI : 10.1051/ro/2009007
Classification : 05C45
Mots clés : graph theory, claw-free graphs, almost claw-free graphs, hamiltonicity, matching
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Abbas, Moncef; Benmeziane, Zineb. Hamiltonicity in partly claw-free graphs. RAIRO - Operations Research - Recherche Opérationnelle, Tome 43 (2009) no. 1, pp. 103-113. doi : 10.1051/ro/2009007. http://www.numdam.org/articles/10.1051/ro/2009007/

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