Spectrum of 3-uniform 6-and 9-cycle systems over Kv(3) - I

We consider edge decompositions of K-v((3)) - I, the complete 3-uniform hypergraph of order v minus a set of v/3 mutually disjoint edges (1-factor). We prove that a decomposition into tight 6-cycles exists if and only if v equivalent to 0, 3, 6 (mod 12) and v >= 6; and a decomposition into tight 9-cycles exists for all v >= 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)] who settled the case of K-v((3)).(c) 2023 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons .org /licenses/by-nc-nd/4.0/).