DECOMPOSING COMPLETE 3-UNIFORM HYPERGRAPH Kn³ INTO 7-CYCLES.

We use the Katona-Kierstead definition of a Hamiltonian cycle in a uniform hypergraph. A decomposition of complete fc-uniform hypergraph K_n^kinto Hamiltonian cycles was studied by Bailey-Stevens and Meszka-Rosa. For n = 2,4, 5 (mod 6), we design an algorithm for decomposing the complete 3-uniform hypergraphs into Hamiltonian cycles by using the method of edge-partition. A decomposition of K_n³ into 5-cycles has been presented for all admissible n ≤ 17, and for all n = 4m + 1 when m is a positive integer. In general, the existence of a decomposition into 5-cycles remains open. In this paper, we show if 42 Ι (n - 1)(n- 2) and if there exist λ = (n-1)(n-2)/42 sequences (k_i0,k_i1,...,k_i6) on D_all(n), then K_n(³) can be decomposed into 7-cycles. We use the method of edge-partition and cycle sequence. We find a decomposition of K₃₇(³) and K₄₃(³ ) into 7-cycles. [ABSTRACT FROM AUTHOR]