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arXiv · 2410.02109

Decompositions of the wreath product of certain directed graphs into directed hamiltonian cycles

Alice Lacaze-Masmonteil
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Abstract

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.

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Alice Lacaze-Masmonteil. 2024-10-03. Decompositions of the wreath product of certain directed graphs into directed hamiltonian cycles. https://arxiv.org/abs/2410.02109

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