We obtain lower and upper bounds for the maximum weight of a directed cut in the classes of weighted digraphs and weighted acyclic digraphs as well as in some of their subclasses. We compare our results with those obtained for the maximum size of a directed cut in unweighted digraphs. In particular, we show that a lower bound obtained by Alon, Bollobas, Gyafas, Lehel and Scott (J Graph Th 55(1) (2007)) for unweighted acyclic digraphs can be extended to weighted digraphs with the maximum length of a cycle being bounded by a constant and the weight of every arc being at least one. We state a number of open problems.

翻译：本文研究了加权有向图、加权无环有向图及其部分子类中有向割的最大权重的上下界。我们将所得结果与未加权有向图中最大有向割规模的结果进行了比较。特别地，我们证明Alon、Bollobás、Gyárfás、Lehel和Scott（《图论杂志》第55卷第1期，2007年）针对未加权无环有向图得到的一个下界可以推广到最大圈长有常数界且每条弧权重至少为1的加权有向图。文章最后提出了一系列未解决问题。