Decomposition of K2n into n-1 Hamiltonian Cycles and a perfect matching Mi

作     者：Zhaodi Xu 1 , Xiaoyi Li 1 , Wanxi Chou 2 1. School of Mathematics and Systems Science, Shenyang Normal University, Shenyang, 110034, China. 2 School of Civil Engineering and Architecture, Anhui University of Science and Technology, Huainan Anhui 232001. China. 

会议名称：《第24届中国控制与决策会议》

会议日期：2012年

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

基　　金：supported by National Nature Science Foundation under Grant 10471096 

关 键 词：complete graph prefect matching Hamiltonian cycle factorization even order 

摘      要：Theorem on 2-factorization of complete graph K 2n of even order is proved. Foundamental concepts of 1-factorization and 2-factorization of complete graphs K 2n are described. Construct the edge matrix of the complete graph K 2n edge coloring has been followed Thus the rectangular matrix has been composed by 1-factor of 2n-1 . Determine the collocation programming which is let 2n-1 1-factor combined with n-1 2-factor and 1 1-factor and generated cycles for each 2-factor , In accordance with the different Programming, The process which let E（G） divide into n-1 frontier set of Hamiltonian cycles and 1 1-factor .The entire procedure of 2-factorization of complete graphs K 10 K 12 and K 14 is presented.