About the Katona-Kierstead definition of a Hamiltonian cycles in a uniform hypergraph, a decomposition of complete k-uniform hypergraph (K_n)~(k) into Hamiltonian cycles studied by Bailey-Stevens and Meszka-Rosa. For n = 2, 4, 5 (mod 6), we design algorithm for decomposing the complete 3-uniform hypergraphs into Hamiltonian cycles by using the method of edge-partition. A decomposition of (K_n)~(3) into 5-cycles has been presented for all admissible n ≤17, and for all n = 4~m + 1, m is a positive integer. In general, the existence of a decomposition into 5-cycles remains open. In this paper, we use the method of edge-partition and cycle sequence proposed by Jirimutu and Wang. We find a decomposition of (K_(20))~(3) into 5-cycles.
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