The 3-Connected Graphs with Exactly Three Non-Essential Edges
β Scribed by James Oxley; Haidong Wu
- Publisher
- Springer Japan
- Year
- 2004
- Tongue
- English
- Weight
- 352 KB
- Volume
- 20
- Category
- Article
- ISSN
- 0911-0119
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π SIMILAR VOLUMES
## Abstract It is shown that with one small exception, the 3βconnected graphs admitting longest cycles that contain less than four contractible edges of the parent graph are the members of three closely related infinite families. Β© 1993 John Wiley & Sons, Inc.
## Abstract It is shown that if __G__ is a 3βconnected graph with |__V(G)__| β₯ 10, then, with the exception of one infinite class based on __K__~3,__p__~, it takes at least four vertices to cover the set of contractible edges of __G__. Β© 1993 John Wiley & Sons, Inc.
## Abstract In this paper, we show that if a 3βconnected graph __G__ other than __K__~4~ has a vertex subset __K__ that covers the set of contractible edges of __G__ and if |__K__| 3 and |__V(G)__| 3|__K__| β 1, then __K__ is a cutset of __G__. We also give examples to show that this result is best