Geodesic
Extension of several sufficient conditions for Hamiltonian graphs
Discussiones Mathematicae. Graph Theory, Tome 26 (2006) no. 1, pp. 23-39

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Let G be a 2-connected graph of order n. Suppose that for all 3-independent sets X in G, there exists a vertex u in X such that |N(X∖u)|+d(u) ≥ n-1. Using the concept of dual closure, we prove that
Keywords: hamiltonian graph, dual closure, neighborhood closure 
Ainouche, Ahmed. Extension of several sufficient conditions for Hamiltonian graphs. Discussiones Mathematicae. Graph Theory, Tome 26 (2006) no. 1, pp. 23-39. http://geodesic.mathdoc.fr/item/DMGT_2006_26_1_a2/
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