McCuaig, W., Cycles through edges in cyclically k-connected cubic graphs
Cycles through five edges in 3-connected cubic graphs
β Scribed by R. E. L. Aldred; D. A. Holton
- Publisher
- Springer Japan
- Year
- 1987
- Tongue
- English
- Weight
- 673 KB
- Volume
- 3
- Category
- Article
- ISSN
- 0911-0119
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
## Abstract A necessary and sufficient condition is obtained for a set of 12 vertices in any 3βconnected cubic graph to lie on a common cycle.
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
Let f (n) be the minimum number of cycles present in a 3-connected cubic graph on n vertices. In 1986, C. A. Barefoot, L. Clark, and R. Entringer (Congr. Numer. 53, 1986) showed that f (n) is subexponential and conjectured that f (n) is superpolynomial. We verify this by showing that, for n sufficie