单循环赛赛程安排的一个图论方法  

A Way of Graph Theory of the Competitive Procedure Arrangement for Single Cyclic Match

作　　者：唐保祥[1] 

机构地区：[1]天水师范学院数学系,甘肃天水741001

出　　处：《数学的实践与认识》2004年第5期120-125,共6页Mathematics in Practice and Theory

摘　　要：利用图论的边着色理论建立了一个赛程安排的数学模型 .首先建立 n支球队与完全图 Kn的 n个顶点间的一一对应 ,把球队 Ai和 Aj间的比赛关系抽象成 Kn的顶点 i和 j间的边 ( i,j) .然后分别构造出了图K2 m- 1和 K2 m的正常 2 m-1边着色 .从而给出了各球队每两场比赛间得到的休整时间最均等 ,休整的间隔场次数达到上限值 n2A mathematical model of the competitive procedure arrangement is designed in this article by using the edge coloring method of graph theory. The correspondence among n apexes one by one between n contingents of teams and complete graph Kn is firstly made. Therefore, the edge (i,j) between the apex I and the apex j of the apexes of Kn is drawn from the competitive relation between Team Ai and Team Aj. Then the normal ″2m-1″ edge coloring for graph K 2m-1 and graph K 2m are respectively constructed. Thus the conclusion is drawn that the time of rest and reorganization between every two matches of each team is most impartial and that the interval number of the match times of rest and reorganization comes to a competitive procedure arrangement plan of the upper limit value n 2.

关 键 词：单循环 赛程安排 图论 边着色 完全图KN 对集 等价关系 集合的划分 图G的^因子分解 

分 类 号：O157.5[理学—数学]