Extension of several sufficient conditions for Hamiltonian graphs

Ahmed Ainouche

Discussiones Mathematicae Graph Theory, Tome 26 (2006), p. 23-39 / Harvested from The Polish Digital Mathematics Library

Résumé

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 1. G is hamiltonian if and only if its 0-dual closure is either complete or the cycle C₇ 2. G is nonhamiltonian if and only if its 0-dual closure is either the graph $(K_r ∪ Kₛ ∪ Kₜ) ∨ K₂$, 1 ≤ r ≤ s ≤ t or the graph $((n+1)/2)K₁ ∨ K_{(n-1)/2}$. It follows that it takes a polynomial time to check the hamiltonicity or the nonhamiltonicity of a graph satisfying the above condition. From this main result we derive a large number of extensions of previous sufficient conditions for hamiltonian graphs. All these results are sharp.

Détail

Publié le : 2006-01-01

Zbl 1103.05044

EUDML-ID : urn:eudml:doc:270300

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