Hamiltonian cycles passing through matchings in $k$-ary $n$-cubes
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866913590355689472 |
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| author | Liao, Baolai Wang, Fan |
| author_facet | Liao, Baolai Wang, Fan |
| contents | As we all know, the $k$-ary $n$-cube is a highly efficient interconnect network topology structure. It is also a concept of great significance, with a broad range of applications spanning both mathematics and computer science. In this paper, we study the existence of Hamiltonian cycles passing through prescribed matchings in $k$-ary $n$-cubes, and obtain the following result. For $n\geq5$ and $k\geq4$, every matching with at most $4n-20$ edges is contained in a Hamiltonian cycle in the $k$-ary $n$-cube. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_19482 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Hamiltonian cycles passing through matchings in $k$-ary $n$-cubes Liao, Baolai Wang, Fan Combinatorics 05C38, 05C45 As we all know, the $k$-ary $n$-cube is a highly efficient interconnect network topology structure. It is also a concept of great significance, with a broad range of applications spanning both mathematics and computer science. In this paper, we study the existence of Hamiltonian cycles passing through prescribed matchings in $k$-ary $n$-cubes, and obtain the following result. For $n\geq5$ and $k\geq4$, every matching with at most $4n-20$ edges is contained in a Hamiltonian cycle in the $k$-ary $n$-cube. |
| title | Hamiltonian cycles passing through matchings in $k$-ary $n$-cubes |
| topic | Combinatorics 05C38, 05C45 |
| url | https://arxiv.org/abs/2411.19482 |