赛程安排的图论模型——2002年全国大学生数学建模竞赛D题

The Graph Model of Match Scheduling

通过建立赛程安排的图论模型 ,圆满解决了 2 0 0 2年全国大学生数学建模竞赛D题的前三个问题。提出了对于任意n支球队进行单循环比赛的赛程编制方法 ,该方法简单易行 ,只须手工编排 ,并证明了该方法编制的赛程使得各队每两场比赛最小相隔的场次数达到了理论上限。

Establishing the graph model of match scheduling, the first three questions of problem D of 2002's Chinese mathematical contest in modeling are solved satisfactorily. A method to schedule a single-round robin of N teams is proposed. The method is simple and it can be done by hand. Moreover, the following conclusion is proved: In the match schedule made by the method, the minimum number of matches between every two matches of each team reaches the theoretical upper bound.