Completing the solution of the directed Oberwolfach problem with two tables
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866909291584159744 |
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| author | Horsley, Daniel Lacaze-Masmonteil, Alice |
| author_facet | Horsley, Daniel Lacaze-Masmonteil, Alice |
| contents | We address the last outstanding case of the directed Oberwolfach problem with two tables of different lengths. Specifically, we show that the complete symmetric directed graph $K^*_n$ admits a decomposition into spanning subdigraphs comprised of two vertex-disjoint directed cycles of length $t_1$ and $t_2$, respectively, where $t_1\in \{4,6\}$, $t_2$ is even, and $t_1+t_2\geqslant 14$. In conjunction with recent results of Kadri and Šajna, this gives a complete solution to the directed Oberwolfach problem with two tables of different lengths. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_10448 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Completing the solution of the directed Oberwolfach problem with two tables Horsley, Daniel Lacaze-Masmonteil, Alice Combinatorics We address the last outstanding case of the directed Oberwolfach problem with two tables of different lengths. Specifically, we show that the complete symmetric directed graph $K^*_n$ admits a decomposition into spanning subdigraphs comprised of two vertex-disjoint directed cycles of length $t_1$ and $t_2$, respectively, where $t_1\in \{4,6\}$, $t_2$ is even, and $t_1+t_2\geqslant 14$. In conjunction with recent results of Kadri and Šajna, this gives a complete solution to the directed Oberwolfach problem with two tables of different lengths. |
| title | Completing the solution of the directed Oberwolfach problem with two tables |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2408.10448 |