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arXiv · 2408.10448

Completing the solution of the directed Oberwolfach problem with two tables

Daniel Horsley·Alice Lacaze-Masmonteil
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Abstract

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 \v{S}ajna, this gives a complete solution to the directed Oberwolfach problem with two tables of different lengths.

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Daniel Horsley, Alice Lacaze-Masmonteil. 2024-08-19. Completing the solution of the directed Oberwolfach problem with two tables. https://arxiv.org/abs/2408.10448

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