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
β¦ LIBER β¦
Lower bounds of length of longest cycles in graphs involving neighborhood unions
β Scribed by Xin Liu
- Publisher
- Elsevier Science
- Year
- 1997
- Tongue
- English
- Weight
- 593 KB
- Volume
- 169
- Category
- Article
- ISSN
- 0012-365X
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## Abstract For a graph __G__, let __p(G)__ denote the order of a longest path in __G__ and __c(G)__ the order of a longest cycle in __G__, respectively. We show that if __G__ is a 3βconnected graph of order __n__ such that $\textstyle{\sum^{4}\_{i=1}\,{\rm deg}\_{G}\,x\_{i} \ge {3\over2}\,n + 1}$