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The 3-Connected Graphs with Exactly Three Non-Essential Edges

✍ 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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πŸ“œ SIMILAR VOLUMES


The 3-connected graphs having a longest
✍ R. E. L. Aldred; Robert L. Hemminger; Katsuhiro Ota πŸ“‚ Article πŸ“… 1993 πŸ› John Wiley and Sons 🌐 English βš– 570 KB

## Abstract It is shown that with one small exception, the 3‐connected 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.

Covering contractible edges in 3-connect
✍ Robert L. Hemminger; Xingxing Yu πŸ“‚ Article πŸ“… 1993 πŸ› John Wiley and Sons 🌐 English βš– 272 KB πŸ‘ 1 views

## Abstract It is shown that if __G__ is a 3‐connected 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.

3-connected graphs with non-cut contract
✍ Xingxing Yu πŸ“‚ Article πŸ“… 1994 πŸ› John Wiley and Sons 🌐 English βš– 493 KB πŸ‘ 1 views

## Abstract In this paper, we show that if a 3‐connected 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__| βˆ’ 1, then __K__ is a cutset of __G__. We also give examples to show that this result is best