✦ LIBER ✦
On a Hamiltonian Cycle in Which Specified Vertices Are Uniformly Distributed
✍ Scribed by Atsushi Kaneko; Kiyoshi Yoshimoto
- Publisher
- Elsevier Science
- Year
- 2001
- Tongue
- English
- Weight
- 191 KB
- Volume
- 81
- Category
- Article
- ISSN
- 0095-8956
No coin nor oath required. For personal study only.
✦ Synopsis
Let G be a graph with n vertices and minimum degree at least nÂ2, and let d be a positive integer such that d nÂ4. We define a distance between two vertices as the number of edges of a shortest path joining them. In this paper, we show that, for any vertex subset A with at most nÂ2d vertices, there exists a Hamiltonian cycle in which the distance between any two vertices of A is at least d.