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Decomposing Complete 3-uniform Hypergraph K58 into 7-cycles with Computer Aid

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DOI: 10.25236/icmcs.2019.025


Narisu, Meiling Guan and Jirimutu

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On the basic of the definition of Hamiltonian cycle defined by Katona-Kierstead and Jianfang Wang independently. Some domestic and foreign researchers study the decomposition of complete 3-uniform hypergraph Kn into Hamiltonian cycles and not Hamiltonian cycles. Especially , Bailey Stevens using Clique - finding the decomposition of Kn into Hamiltonian cycles for K7 , K8 . Meszka-Rosa showed that Hamiltonian decompositions of Kn for all admissible n≤32 . Meszka-Rosa proved that a decomposition of Kn into 5-cycles has been presented for all admissible n≤17 , and for all n=4m+1 , m is a positive integer. In general, the existence of a decomposition into l(≥5) -cycles remains open. The authors have given the decomposition of Kn into 7-cycles for n∈{7,8,14,16,22,23,29,37,43,44,50} and has showed if Kn can be decomposition into 7-cycles, then K7n can be decomposition into 7-cycles. In this paper, a decomposition of K58 into 7-cycles is proved using the method of edge-partition and cycle sequence proposed by Jirimutu.


Uniform hypergraph, 7-cycle, Cycle decomposition