α-Resolvable Cycle Systems for Cycle Length 4  

α-可分解4-圈系统(英文)

作　　者：马秀文 田子红 

机构地区：[1]State Key Laboratory of Networking and Switching Technology, Beijing University of Posts and Telecommunications [2]College of Mathematics and Information Science, Hebei Normal University

出　　处：《Journal of Mathematical Research and Exposition》2009年第6期1102-1106,共5页数学研究与评论（英文版）

基　　金：the National Natural Science Foundation of China (No.10971051)

摘　　要：An m-cycle system of order v and index λ, denoted by m-CS(v,λ), is a collection of cycles of length m whose edges partition the edges of λKv. An m-CS(v,λ) is α-resolvable if its cycles can be partitioned into classes such that each point of the design occurs in precisely α cycles in each class. The necessary conditions for the existence of such a design are m|λv(v-1)/2,2|λ(v -1),m|αv,α|λ(v-1)/2. It is shown in this paper that these conditions are also sufficient when m = 4.An m-cycle system of order v and index λ, denoted by m-CS（v,λ）, is a collection of cycles of length m whose edges partition the edges of λKv. An m-CS（v,λ） is α-resolvable if its cycles can be partitioned into classes such that each point of the design occurs in precisely α cycles in each class. The necessary conditions for the existence of such a design are m｜λv（v-1）/2,2｜λ（v -1）,m｜αv,α｜λ（v-1）/2. It is shown in this paper that these conditions are also sufficient when m = 4.

关 键 词：CYCLE cycle system a-resolvable. 

分 类 号：O157.2[理学—数学]