供稿: 孙雯雯;姬玉荣 | 时间: 2019-04-25 | 次数: |
作者单位:集美大学理学院;河南理工大学数学与信息科学学院
摘要:研究完全二部图Kn,n的循环m-圈分解的存在性问题.利用差的方法构造完全二部图Kn,n的循环m-圈分解的初始圈.对于m≡0(mod8)且m≥8这种情况,证明当n≡0,m/2,m,3m/2(mod2m)时完全二部图Kn,n存在循环m-圈分解;对于m≡0(mod8),m≥8且m/4无平方因子这种情况,证明了完全二部图Kn,n存在循环m-圈分解的充分必要条件是n≡0,m/2(modm).
基金:河南省自然科学基金资助项目(0611055600);福建省教育厅资助项目(JA07143);
DOI:10.16186/j.cnki.1673-9787.2008.06.007
分类号:O157.5
Abstract:The existence problem for cyclic m-cycle decompositions of complete bipartite graphs Kn, n is discussed.Different methods are used to construct the base cycles of cyclic m-cycle decompositions in complete bipartite graphs Kn, n.For m≡0 (mod8) and m≥8, cyclic m-cycle decompositions of complete bipartite graphs Kn, n are constructed seperately when n≡0, m/2, m and 3m/2 (mod2m) .It shows that for m≡0 (mod8) , m≥8 and m/4 square-free, there exists a cyclic m-cycle decomposition of complete bipartite graph Kn, n if and only if n≡0, m/2 (modm) .