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arXiv · 2212.11058

Spectrum of $3$-uniform $6$- and $9$-cycle systems over $K_v^{(3)}-I$

Anita Keszler·Zsolt Tuza
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Abstract

We consider edge decompositions of $K_v^{(3)}-I$, the complete 3-uniform hypergraph of order $v$ minus a 1-factor (parallel class, packing of $v/3$ disjoint edges). We prove that a decomposition into tight 6-cycles exists if and only if $v\equiv 0,3,6$ (mod 12) and $v\geq 6$; and a decomposition into tight 9-cycles exists for all $v\geq 9$ divisible by 3. These results are complementary to the theorems of Akin et al. [Discrete Math. 345 (2022)] and Bunge et al. [Australas. J. Combin. 80 (2021)].

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Anita Keszler, Zsolt Tuza. 2022-12-21. Spectrum of $3$-uniform $6$- and $9$-cycle systems over $K_v^{(3)}-I$. https://arxiv.org/abs/2212.11058

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