On k-step Hamiltonian graphs
For integers k 1, a (p, q)-graph G = (V, E) is said to admit an AL(k)-traversal if there exists a sequence of vertices (v1, v 2,. . .,vp) such that for each i = 1, 2, . . . , p - 1, the distance between vi and vi is k. We call a graph ¿-step Hamiltonian (or say it admits a k-step Hamiltonian tour) i...
| 总结: | For integers k 1, a (p, q)-graph G = (V, E) is said to admit an AL(k)-traversal if there exists a sequence of vertices (v1, v 2,. . .,vp) such that for each i = 1, 2, . . . , p - 1, the distance between vi and vi is k. We call a graph ¿-step Hamiltonian (or say it admits a k-step Hamiltonian tour) if it has an (AL(k)-traversal and d(v1, vp) = k. In this paper, we investigate the k-step Hamiltonicity of graphs. In particular, we show that every graph is an induced subgraph of a k-step Hamiltonian graph for all k 2. |
|---|---|
| ISSN: | 8353026 |