On cubic 2-independent Hamiltonian connected graphs
β Scribed by Tung-Yang Ho; Chun-Nan Hung; Lih-Hsing Hsu
- Publisher
- Springer US
- Year
- 2007
- Tongue
- English
- Weight
- 822 KB
- Volume
- 14
- Category
- Article
- ISSN
- 1382-6905
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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.
In this paper it is shown that any rn-regular graph of order 2rn (rn 3 3), not isomorphic to K, , , , or of order 2rn + 1 (rn even, rn 3 4), is Hamiltonian connected, which extends a previous result of Nash-Williams. As a corollary, it is derived that any such graph contains at least rn Hamiltonian
It is proven that every connected Cayley graph X , of valency at least three, on a Hamiltonian group is either Hamilton laceable when X is bipartite, or Hamilton connected when X is not bipartite.
## Abstract M. Matthews and D. Sumner have proved that of __G__ is a 2βconnected clawβfree graph of order __n__ such that Ξ΄ β§ (__n__ β 2)/3, then __G__ is hamiltonian. We prove that the bound for the minimum degree Ξ΄ can be reduced to __n__/4 under the additional condition that __G__ is not in __F_