完全3-一致超图K_(50)^(3)的7-圈分解  

Decomposing Complete 3-uniform Hypergraph K_(50)^(3) into 7-cycles

作　　者：关美玲 吉日木图[1,2] GUAN Mei-ling;Jirimutu(College of Mathematics,Inner Mongolia University for Nationalities,Tongliao 028043,China;Discrete Mathematics Institute,Inner Mongolia University for Nationalities,Tongliao 028043,China)

机构地区：[1]内蒙古民族大学数学学院,内蒙古通辽028043 [2]内蒙古民族大学离散数学研究所,内蒙古通辽028043

出　　处：《内蒙古民族大学学报（自然科学版）》2018年第2期93-97,共5页Journal of Inner Mongolia Minzu University：Natural Sciences

基　　金：国家自然科学基金资助项目(11161032);内蒙古民族大学研究生科研创新资助项目(NMDSS1730)

摘　　要：在Katona-Kierstead和王建方分别独立定义的Hamiltonian链和圈的定义的基础上.一些国内外学者研究了完全3-一致超图K_n^(3)的Hamiltonian与非Hamiltonian圈分解问题.特别的,Bailey Stevens使用团的方法找到了K(3)7,K(3)8的Hamiltonian圈分解.Meszka-Rosa证明了对于n≤32所有可能值的K_n^(3)可以Hamiltonian圈分解,并介绍了对任意的n≤17和所有n=4m+1,当m是正整数时,K_n^(3)可以5圈分解.一般来说,K_n^(3)的l(l≥5)圈分解问题仍然是公开的.目前已得到n∈{7,8,14,16,22,23,29,37,43,44}时完全3-一致超图K_n^(3)可以7-圈分解,并且若K_n^(3)可以7-圈分解,则K(3)7n也可以7-圈分解.文章使用完全3-一致超图K_n^(3)的边划分和圈序列方法得到了K_(50)^(3)的7-圈分解.On the basis of the definition of Hamiltonian cycle defined by Katona-Kierstead and Jianfang Wang independently,studies on the decomposition of complete 3-uniform hypergraph K(3)n into Hamiltonian cycles and not Hamiltonian cycles have been carried out.Bailey Stevens used Clique-finding for the decomposition of K(3)n into Hamiltonian cycles for K(3)7,K(3)8.Meszka-Rosa showed that Hamiltonian decompositions of K(3)n for all admissible n≤32.Meszka-Rosa proved that a decomposition of K(3)n into 5-cycles has been presented for all admissible n≤17,and for all n=4m+1,where m is a positive integer.In general,the existence of decomposition into l(l≥5)-cycles remains open.We have given the decomposition of K(3)n into 7-cycles for n∈{7,8,14,16,22,23,29,37,43,44}and showed if K(3)n can have decomposition into 7-cycles,then K(3)7n can also have decomposition into 7-cycles.,We demonstrate a decomposition of K(3)50 into 7-cycles by using the method of edge-partition and cycle sequence proposed by Jirimutu.

关 键 词：一致超图 7-圈 圈分解 

分 类 号：O157.5[理学—数学]