The complete 3-uniform hypergraph K (3) n of order n has a set V of cardinality n as its vertex set and the set of all 3 element subsets of V as its edge set. For n? 2, let Zn denote the set of integers modulo n. For m > 3, let LC (3) m (respectively, TC (3) m) denote the 3-uniform hypergraph with vertex set Z2m (respectively, Zm) and edge set {2i, 2i+1, 2i+2: i? 0, 1, 2,. . . , m-1} (respectively, {i, i+1, i+2: i? Zm}). Any hypergraph isomorphic to LC (3) m (respectively, TC (3) m) is a 3-uniform loose m-cycle (respectively, 3-uniform tight m-cycle). A decomposition of K (3) n is a partition of the edge set of K (3) n. We show that there exists a decomposition of K (3) n into subhypergraphs isomorphic to LC (3) 7 if and only if n? 14 and n? 0, 1 or 2 (mod 7). Next, we show that, for? ? 1 and m? 8, 16, 20, 28, 32, 40, 44, there exists a decomposition of K (3) 2? m into subhypergraphs isomorphic to TC (3) m.
Sivakaran et al. (Wed,) studied this question.