Let G be a connected graph, where k 2. S. Smith conjectured that every two longest cycles of G have at least k vertices in common. In this note, we show that every two longest cycles meet in at least ck 3Γ5 vertices, where cr0.2615. ## 1998 Academic Press In this note, we provide a lower bound on
Intersections of Cycles in\(k\)-Connected Graphs
β Scribed by Chen, Jessica; Chen, Le; Liu, Derrick
- Book ID
- 125345630
- Publisher
- Springer Japan
- Year
- 2014
- Tongue
- English
- Weight
- 783 KB
- Volume
- 31
- Category
- Article
- ISSN
- 0911-0119
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
## Abstract We show that every __k__βconnected graph with no 3βcycle contains an edge whose contraction results in a __k__βconnected graph and use this to prove that every (__k__ + 3)βconnected graph contains a cycle whose deletion results in a __k__βconnected graph. This settles a problem of L. Lo
## Abstract In this article, we prove the following theorem. Let __k__ββ₯β3 be an integer, __G__ be a __k__βconnected graph with minimum degree __d__ and __X__ be a set of __k__β+β1 vertices on a cycle. Then __G__ has a cycle of length at least min {2d,|V(G)|} passing through __X__. This result give