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...
| Published in: | Journal of Combinatorial Mathematics and Combinatorial Computing |
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| Format: | Article |
| Language: | English |
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Charles Babbage Research Centre
2014
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| Online Access: | https://www.scopus.com/inward/record.uri?eid=2-s2.0-84906237290&partnerID=40&md5=f50a42137bc62bf7addb2626bb190766 |
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2-s2.0-84906237290 |
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2-s2.0-84906237290 Lau G.-C.; Lee S.-M.; Schaffer K.; Tong S.-M.; Lui S. On k-step Hamiltonian graphs 2014 Journal of Combinatorial Mathematics and Combinatorial Computing 90 https://www.scopus.com/inward/record.uri?eid=2-s2.0-84906237290&partnerID=40&md5=f50a42137bc62bf7addb2626bb190766 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. Charles Babbage Research Centre 8353026 English Article |
| author |
Lau G.-C.; Lee S.-M.; Schaffer K.; Tong S.-M.; Lui S. |
| spellingShingle |
Lau G.-C.; Lee S.-M.; Schaffer K.; Tong S.-M.; Lui S. On k-step Hamiltonian graphs |
| author_facet |
Lau G.-C.; Lee S.-M.; Schaffer K.; Tong S.-M.; Lui S. |
| author_sort |
Lau G.-C.; Lee S.-M.; Schaffer K.; Tong S.-M.; Lui S. |
| title |
On k-step Hamiltonian graphs |
| title_short |
On k-step Hamiltonian graphs |
| title_full |
On k-step Hamiltonian graphs |
| title_fullStr |
On k-step Hamiltonian graphs |
| title_full_unstemmed |
On k-step Hamiltonian graphs |
| title_sort |
On k-step Hamiltonian graphs |
| publishDate |
2014 |
| container_title |
Journal of Combinatorial Mathematics and Combinatorial Computing |
| container_volume |
90 |
| container_issue |
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| doi_str_mv |
|
| url |
https://www.scopus.com/inward/record.uri?eid=2-s2.0-84906237290&partnerID=40&md5=f50a42137bc62bf7addb2626bb190766 |
| description |
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. |
| publisher |
Charles Babbage Research Centre |
| issn |
8353026 |
| language |
English |
| format |
Article |
| accesstype |
|
| record_format |
scopus |
| collection |
Scopus |
| _version_ |
1818940563973472256 |