The Decomposition Of Complete 3-Uniform Hypergraph And Its Application

With the emergence of informational science, hypergraphs serves as useful mathematical models for a broad range of applications such as network, database theory, clustering and chemistry. In this paper, on the basic of the definition of Hamiltonian chain and Hamiltonian cycle by Katona-Kierstead and Jianfang Wang-Lee T. Tony independently. On this basis, we make some research and discussion, the details are as follows.The first part simply contains the basic concepts of general graphs and hypergraphs, and the development of the decomposition of complete k-uniform hypergraph Kn(k) into Hamiltonian cycles and not Hamiltonian cycles at home and abroad.The second part contains the decomposition of complete 3-uniform hypergraphs Kn(3) into not Hamiltonian cycles. Because of the existing conclusions are less. We combine the knowledge of the decomposition of complete 3-uniform hypergraph Kn(3) and give the definition of l-cycle. Furthermore, we study the decomposition of complete 3-uniform hypergraph Kn(3) into 5-cycles and 7-cycles and show that K5n(3) and K7n(3) can be decomposed into 5-cycles and 7-cycles.The third part studies the application of (not Hamiltonian) cycle decomposition in the combinational design and gives the results of S (3, C5, n) and S (3, C7,n).