A tournament $T=(V,A)$ is called cycle Mengerian (CM) if it satisfies the minimax relation on packing and covering cycles, for every nonnegative integral weight function defined on A. The purpose of this series of two papers is to show that a tournament is CM iff it contains none of four Möbius ladders as a subgraph; such a tournament is referred to as Möbius-free. In the first paper we have given a structural description of all Möbius-free tournaments, and have proved that every CM tournament is Möbius-free. In this second paper we establish the converse by using our structural theorems and linear programming approach.

中文翻译：

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无错误地对锦标赛进行排名II：Minimax关系

比赛 $Ť=（V，\mathrm{一种}）$如果满足A上定义的每个非负积分权重函数，如果满足包装和覆盖周期的极小极大关系，则称为“周期Mengerian（CM）”。这一系列两篇论文的目的是表明锦标赛是CM，如果它不包含四个Möbius梯子作为子图，则为CM。这样的锦标赛被称为无哥比乌斯锦标赛。在第一篇论文中，我们对所有无Möbius的锦标赛进行了结构化描述，并证明了每一个CM锦标赛都不含Möbius。在第二篇论文中，我们使用结构定理和线性规划方法建立了逆。