ملخص: Let G = (V, E) be a k-connected graph of order n. For S [subset of] V, let N(S) be its neighborhood set and let J(S) = {u [negated set membership] S | N(u) [superset of or equal to] S} if |S| [ges] 2 and J(S) = 0 otherwise. If there exists some s, 1 [les] s [les] k, such that every independent set X of s + 1 vertices has a vertex u satisfying |N(X[beta]{u})| + |N(u) [union or logical sum] J(X)[beta]{u})| [ges] n, then G is hamiltonian. From this main theorem, we derive new sufficient conditions for hamiltonian graphs. Some of these results are improvements and/or generalizations of various known results. In particular, sufficient conditions of Ore (1960), Chvatal and Erdos (1972), Fraisse (1986) and E. Flandrin et al. (1991) are easily derived.

لغة: إنجليزية
الموضوع الرياضيات

الكلمات الدالة:
Hamiltonian cycle
Hamiltonian path
Neighborhood union
Neighborhood intersection