A generalization of Ore's Theorem involving neighborhood unions
نویسندگان
چکیده
Let G be a graph of order n. Settling conjectures of Chen and Jackson, we prove the following generalization of Ore’s Theorem: If G is 2-connected and )N(u)u N(v)1 >:n for every pair of nonadjacent vertices a, u, then either G is hamiltonian, or G is the Petersen graph, or G belongs to one of three families of exceptional graphs of connectivity 2.
منابع مشابه
Neighborhood generalization unions and a of Dirac’s theorem
Faudree, R.J., R.J. Gould, M.S. Jacobson and L.M. Lesniak, Neighborhood unions and a generalization of Dirac’s theorem, Discrete Mathematics 105 (1992) 61-71. Dirac proved that if each vertex of a graph G of order n 23 has degree at least n/2, then the graph is Hamiltonian. This result will be generalized by showing that if the union of the neighborhoods of each pair of vertices of a 2connected...
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ورودعنوان ژورنال:
- Discrete Mathematics
دوره 122 شماره
صفحات -
تاریخ انتشار 1993