单循环赛程编排的数学模型

Mathematical model of monocyclic match schedule

作者用邻接矩阵的方式建立了单循环赛程编排的数学模型,给出了尽量公平原则的最优上限和下限,并以图论方法详细描述了n为偶数和n为奇数情形均衡解编排的全部过程。作为特例,得到了n=5,8,9情形的均衡解。

In the paper, the author establishes a mathematical model about the monocyclic match schedule by using the method of adjacency matrix, points out the optimal lower and upper bounds under the impartiality-first principle, and explains in detail the whole process of how to get the equilibrium solution by graph theory method when n is odd or even. As a case study, the paper obtains the equilibrium solutions when n is 5, 8 and 9, respectively.