Jackson, B., H. Li and Y. Zhu, Dominating cycles in regular 3-connected graphs, Discrete Mathematics 102 (1992) 163-176. Let G be a 3-connected, k-regular graph on at most 4k vertices. We show that, for k > 63, every longest cycle of G is a dominating cycle. We conjecture that G is in fact hamilton
A note on dominating cycles in 2-connected graphs
β Scribed by D. Bauer; E. Schmeichel; H.J. Veldman
- Publisher
- Elsevier Science
- Year
- 1996
- Tongue
- English
- Weight
- 277 KB
- Volume
- 155
- Category
- Article
- ISSN
- 0012-365X
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Nous prouvons une conjecture due & Bondy et Fan. Un cycle C d'un graphe G est dit m-dominant si tout sommet de V(G -C) est a distance au plus m de C. Notre r&t&at est: si G est k-connexe, et si G n'a pas de cycle m-dominant, alors il existe un stable de cardinal k + 1, dont les sommets sont deux 3 d
Vu Dinh, H., On the length of longest dominating cycles in graphs, Discrete Mathematics 121 (1993) 21 l-222. ## A cycle C in an undirected and simple graph if G contains a dominating cycle. There exists l-tough graph in which no longest cycle is dominating. Moreover, the difference of the length
## Abstract A set __S__ of vertices in a graph __G__ is a total dominating set of __G__ if every vertex of __G__ is adjacent to some vertex in __S__. The minimum cardinality of a total dominating set of __G__ is the total domination number Ξ³~t~(__G__) of __G__. It is known [J Graph Theory 35 (2000)
## 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_