On n-hamiltonian graphs
β Scribed by Linda Lesmak
- Book ID
- 107748216
- Publisher
- Elsevier Science
- Year
- 1976
- Tongue
- English
- Weight
- 598 KB
- Volume
- 14
- Category
- Article
- ISSN
- 0012-365X
No coin nor oath required. For personal study only.
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## Abstract A graph __G__ of order at least 2__n__+2 is said to be __n__βextendable if __G__ has a perfect matching and every set of __n__ independent edges extends to a perfect matching in __G__. We prove that every pair of nonadjacent vertices __x__ and __y__ in a connected __n__βextendable graph
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.