Potential forbidden triples implying hamiltonicity: for sufficiently large graphs
Ralph J. Faudree ; Ronald J. Gould ; Michael S. Jacobson
Discussiones Mathematicae Graph Theory, Tome 25 (2005), p. 273-289 / Harvested from The Polish Digital Mathematics Library
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In [1], Brousek characterizes all triples of connected graphs, G₁,G₂,G₃, with Gi=K1,3 for some i = 1,2, or 3, such that all G₁G₂ G₃-free graphs contain a hamiltonian cycle. In [8], Faudree, Gould, Jacobson and Lesniak consider the problem of finding triples of graphs G₁,G₂,G₃, none of which is a K1,s, s ≥ 3 such that G₁G₂G₃-free graphs of sufficiently large order contain a hamiltonian cycle. In [6], a characterization was given of all triples G₁,G₂,G₃ with none being K1,3, such that all G₁G₂G₃-free graphs are hamiltonian. This result, together with the triples given by Brousek, completely characterize the forbidden triples G₁,G₂,G₃ such that all G₁G₂G₃-free graphs are hamiltonian. In this paper we consider the question of which triples (including K1,s, s ≥ 3) of forbidden subgraphs potentially imply all sufficiently large graphs are hamiltonian. For s ≥ 4 we characterize these families.

Publié le : 2005-01-01
EUDML-ID : urn:eudml:doc:270266 
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Ralph J. Faudree; Ronald J. Gould; Michael S. Jacobson. Potential forbidden triples implying hamiltonicity: for sufficiently large graphs. Discussiones Mathematicae Graph Theory, Tome 25 (2005) pp. 273-289. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1281/

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