完全3-一致超图K_(41)^((3))的5-圈分解  

A Decomposition of Complete 3-uniform Hypergraph K_(41)^((3)) into 5-cycles

作　　者：冯伟[1,2] Enkhtsolmon 尹艳 徐春雷[1,2] 李冠儒[1,2] FENG Wei;Enkhtsomon;YIN Yan;XU Chunei;LI Guanru(College of Mathematical Sciences,Inner Mongolia Minzu University,Tongliao 028043,China;Discrete Mathematics Institute,Inner Mongolia Minzu University,Tongliao 028043,China;Institute of Mathematics and Digital Technology,Mongolian Academy of Sciences,Ulaanbaatar 13330,Mongolia;Tongliao City Experimental Primary School,Tongliao 028000,China)

机构地区：[1]内蒙古民族大学数学科学学院,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 [3]蒙古科学院数学与数字技术研究所,蒙古国乌兰巴托13330 [4]通辽市实验小学,内蒙古通辽028000

出　　处：《内蒙古民族大学学报（自然科学版）》2024年第4期9-13,共5页Journal of Inner Mongolia Minzu University：Natural Sciences Edition

基　　金：内蒙古自治区自然科学基金项目(2022LHMS01006);内蒙古自治区直属高校基本科研业务费项目(GXKY22156);内蒙古民族大学博士科研启动基金项目(BSZ013,BSZ014,BS643)。

摘　　要：超图是有限集合的子集系统,它与数据库有密切关系。从数据库理论来看,圈结构是超图理论中最本质、最基本的结构。超图的圈分解是超图理论中重要的研究内容之一。有研究者对超图的哈密尔顿圈、非哈密尔顿圈分解做了研究。利用超图的圈分解序列与其边划分序列二者之间的关联,对n阶完全3-一致超图存在5-圈分解的公开问题进行了研究,验证了n=41时公开问题成立。A hypergraph is a subset system of finite sets,which is closely related to databases.From the per-spective of database theory,the cycle-structure is the most essential and fundamental structure in hypergraph theory.The cycle decomposition of hypergraphs is one of the important research topics in hypergraph theory.Researchers have studied the Hamiltonian cycle and non-Hamiltonian cycle decomposition of hypergraphs.By utilizing the corre-lation between the cycle decomposition sequence of a hypergraph and its edge partition sequence,it is investigated that the open problem of decomposing the complete 3-uniform hypergraph with n order into 5-cycles,and it is proved that the validity of the open problem when n=41.

关 键 词：完全3-一致超图 圈分解 5-圈分解 

分 类 号：O157.5[理学—数学]