In this paper, we show that every 2-connected, k-regular claw-free graph on n vertices contains a cycle of length at least min {4k-2, n} (k >~ 8), and this result is best possible. ## I. Introduction All graphs considered here are undirected and finite, without loops or multiple edges. A graph G is
Longest cycles in r-regular r-connected graphs
โ Scribed by Brad Jackson; T.D Parsons
- Publisher
- Elsevier Science
- Year
- 1982
- Tongue
- English
- Weight
- 777 KB
- Volume
- 32
- Category
- Article
- ISSN
- 0095-8956
No coin nor oath required. For personal study only.
๐ SIMILAR VOLUMES
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 3ร5 vertices, where cr0.2615. ## 1998 Academic Press In this note, we provide a lower bound on
If rjn ร 1 and rn is even, then K n can be expressed as the union of t nร1 r edgedisjoint isomorphic r-regular r-connected factors.
Jackson, B., H. Li and Y. Zhu, Dominating cycles in regular 3-connected graphs, Discrete Mathematics 102 (1992) 163-176. Let G be a 3-connected, k-regular graph on at most 4k vertices. We show that, for k > 63, every longest cycle of G is a dominating cycle. We conjecture that G is in fact hamilton
We show in this paper that for k Z-63, every 3-connected, k-regular simple graph on at most yk vertices is hamiltonian.