Decompositions of the wreath product of certain directed graphs into directed hamiltonian cycles
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866929525464498176 |
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| author | Lacaze-Masmonteil, Alice |
| author_facet | Lacaze-Masmonteil, Alice |
| contents | We affirm several special cases of a conjecture that first appears in Alspach et al.~(1987) which stipulates that the wreath (lexicographic) product of two hamiltonian decomposable directed graphs is also hamiltonian decomposable. Specifically, we show that the wreath product of hamiltonian decomposable directed graph $G$, such that $|V(G)|$ is even and $|V(G)|\geqslant 3$, with a directed $m$-cycle such that $m \geqslant 4$ or the complete symmetric directed graph on $m$ vertices such that $m\geqslant 3$, is hamiltonian decomposable. We also show the wreath product of a directed $n$-cycle, where $n$ is even, with a directed $m$-cycle, where $m \in \{2,3\}$, is not hamiltonian decomposable. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_02109 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Decompositions of the wreath product of certain directed graphs into directed hamiltonian cycles Lacaze-Masmonteil, Alice Combinatorics We affirm several special cases of a conjecture that first appears in Alspach et al.~(1987) which stipulates that the wreath (lexicographic) product of two hamiltonian decomposable directed graphs is also hamiltonian decomposable. Specifically, we show that the wreath product of hamiltonian decomposable directed graph $G$, such that $|V(G)|$ is even and $|V(G)|\geqslant 3$, with a directed $m$-cycle such that $m \geqslant 4$ or the complete symmetric directed graph on $m$ vertices such that $m\geqslant 3$, is hamiltonian decomposable. We also show the wreath product of a directed $n$-cycle, where $n$ is even, with a directed $m$-cycle, where $m \in \{2,3\}$, is not hamiltonian decomposable. |
| title | Decompositions of the wreath product of certain directed graphs into directed hamiltonian cycles |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2410.02109 |