Longest Cycles in 3-connected Graphs with Given Independence Number
β Scribed by Y. Manoussakis
- Book ID
- 106047788
- Publisher
- Springer Japan
- Year
- 2009
- Tongue
- English
- Weight
- 113 KB
- Volume
- 25
- Category
- Article
- ISSN
- 0911-0119
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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__~__