Hong HUO, Ling Qi ZHAO, Wei FENG, Yuan Sheng YANG, Jirimutu
Based on the definition of a Hamiltonian cycle gived by Janfang Wang and Tony Lee, and the definition of a Hamiltonian chain gived by Katona–Kierstead in a uniform hypergraph, recently, many domestic and foreign researchers studied the hamiltonian cycle decomposition of the uniform hypergraphs Kn(3), and obtained a series of results. Especially, Bailey–Stevens and Meszka–Rosa studied the hamiltonian cycle decomposition of the complete 3-uniform hypergraphs Kn(3), showed the result of hamiltonian cycle decomposition of Kn(3) for n = 6k + 1, 6k + 2 (k= 1, 2, 3, 4, 5). In this paper, using the methods of edge-partition proposed by Jirimutu, we will continue study Hamiltonian decomposition of the complete 3-uniform hypergraphs Kn(3), design an algorithm of Hamiltonian decompositions of Kn(3), and use the algorithm, we show the result of hamiltonian cycle decomposition of Kn(3) for n = 6k + 2, 6k + 4 (k= 1, 2, 3, 4, 5, 6, 7), n = 6k+5 (k= 1, 2, 3, 4, 5, 6). These results improve results of Hamiltonian decompositions from all admissible n ≤ 32 (Meszka–Rosa's paper) to all admissible n ≤ 46 and n = 43.