Decomposing Complete 3-Uniform Hypergraphs into Cycles  

作　　者：Guanru LI Yiming LEI Yuansheng YANG Jirimutu 

机构地区：[1]College of Mathematics,Institute of Discrete Mathematics of Inner Mongolia University for the Nationalities [2]School of Computer Science and Technology,Dalian University of Technology

出　　处：《Journal of Mathematical Research with Applications》2016年第1期9-14,共6页数学研究及应用（英文版）

基　　金：Supported by the National Natural Science Foundation of China(Grant No.11161032)

摘　　要：The problem of decomposing a complete 3-uniform hypergraph into Hamilton cycles was introduced by Bailey and Stevens using a generalization of Hamiltonian chain to uniform hypergraphs by Katona and Kierstead. Decomposing the complete 3-uniform hypergraphs Kn（3） into k-cycles （3 ≤ k 〈 n） was then considered by Meszka and Rosa. This study investigates this problem using a difference pattern of combinatorics and shows that Kn·5m（3） can be decomposed into 5-cycles for n ∈ {5, 7, 10, 11, 16, 17, 20, 22, 26} using computer programming.The problem of decomposing a complete 3-uniform hypergraph into Hamilton cycles was introduced by Bailey and Stevens using a generalization of Hamiltonian chain to uniform hypergraphs by Katona and Kierstead. Decomposing the complete 3-uniform hypergraphs Kn（3） into k-cycles （3 ≤ k 〈 n） was then considered by Meszka and Rosa. This study investigates this problem using a difference pattern of combinatorics and shows that Kn·5m（3） can be decomposed into 5-cycles for n ∈ {5, 7, 10, 11, 16, 17, 20, 22, 26} using computer programming.

关 键 词：uniform hypergraph 5-cycle cycle decomposition 

分 类 号：O157.5[理学—数学] O314[理学—基础数学]