Longest cycles in 3-connected graphs
β Scribed by B. Wei
- Book ID
- 108316040
- Publisher
- Elsevier Science
- Year
- 1997
- Tongue
- English
- Weight
- 395 KB
- Volume
- 170
- Category
- Article
- ISSN
- 0012-365X
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π SIMILAR VOLUMES
We show that if G is a 3-connected graph of order at least seven, then every longest path between distinct vertices in G contains at least two contractible edges. An immediate corollary is that longest cycles in such graphs contain at least three contractible edges. We consider only finite undirect
## Abstract For a graph __G__, we denote by __d__~__G__~(__x__) and ΞΊ(__G__) the degree of a vertex __x__ in __G__ and the connectivity of __G__, respectively. In this article, we show that if __G__ is a 3βconnected graph of order __n__ such that __d__~__G__~(__x__) + __d__~__G__~(__y__) + __d__~__
## 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 $\textstyle{\sum^{4}\_{i=1}\,{\rm deg}\_{G}\,x\_{i} \ge {3\over2}\,n + 1}$