Spectrum of 3-uniform 6- and 9-cycle systems over [formula omitted].

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 ≡ 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). [ABSTRACT FROM AUTHOR]