In this note, w e give a short proof of a stronger version of the following theorem: Let G be a 2-connected graph of order n such that for any independent set {u, u , w}, then G is hamiltonian. 0 1996 John
Two theorems on Hamiltonian graphs
β Scribed by A. S. Asratyan; N. K. Khachatryan
- Publisher
- SP MAIK Nauka/Interperiodica
- Year
- 1984
- Tongue
- English
- Weight
- 328 KB
- Volume
- 35
- Category
- Article
- ISSN
- 0001-4346
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π SIMILAR VOLUMES
## Abstract One of the most fundamental results concerning paths in graphs is due to Ore: In a graph __G__, if deg __x__ + deg __y__ β§ |__V__(__G__)| + 1 for all pairs of nonadjacent vertices __x, y__ β __V__(__G__), then __G__ is hamiltonianβconnected. We generalize this result using set degrees.
Suppose G is a graph, F is a l-factor of G. G is called F-Hamiltonian, if there exists a Hamiltonian cycle containing F in G. In this paper, two necessary and sufficient conditions for a general graph and a bipartite graph being F-Hamiltonian are provided, respectively.