In this note, w e give a short proof of a stronger version of the following theorem: Let G be a 2-connected graph of order n such that for any independent set {u, u , w}, then G is hamiltonian. 0 1996 John
A short proof and a strengthening of the Whitney 2-isomorphism theorem on graphs
β Scribed by A.K Kelmans
- Publisher
- Elsevier Science
- Year
- 1987
- Tongue
- English
- Weight
- 887 KB
- Volume
- 64
- Category
- Article
- ISSN
- 0012-365X
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
## Abstract In this note a shortened proof is given for the FaudreeβSchelp theorem on pathβconnected graphs.
proved that if G is a 2-connected graph with n vertices such that d(u)+d(v)+d(w) n+} holds for any triple of independent vertices u, v, and w, then G is hamiltonian, where } is the vertex connectivity of G. In this note, we will give a short proof of the above result.
A simple characterisation of cycles and complete graphs highlights their significance in Brooks' theorem. It then shows that an algorithmic proof of that theorem. usually dealt with in two cases. is in fact covered by one of the cases. ## 1. Some 2-connected graphs Throughout this paper G = (V, E)