Hamiltonian cycles of a connected graph
β Scribed by L. M. Likhtenbaum
- Publisher
- Springer US
- Year
- 1968
- Tongue
- English
- Weight
- 291 KB
- Volume
- 4
- Category
- Article
- ISSN
- 1573-8337
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## Abstract In this paper, we show that every 3βconnected clawβfree graph on n vertices with Ξ΄ β₯ (__n__ + 5)/5 is hamiltonian. Β© 1993 John Wiley & Sons, Inc.
## 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_
## 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.
We prove the following theorem. "I'neorem. If G is a balanced bipartite graph with bipartition (A, B), [A I = IBI = n, such that for any x ~ A, y ~ B, d(x) + d(y) >>-n + 2, then for any (nl, n2), ni >I 2, n -----n I + hE, G contains two independent cycles of lengths 2nl and 2n2.