In this paper we consider the digraph width measures directed path-width, directed tree-width, directed feedback vertex set number, directed feedback arc set number, cycle rank, DAG-depth, DAG-width and Kelly-width of recursively defined digraphs. While the minimization problem for these width measures is generally NP-hard, we prove that it is computable in linear time for all these parameters, except for Kelly-width, when restricted to directed co-graphs. As an important combinatorial tool, we show how these measures can be computed for the disjoint union, order composition, directed union, and series composition of two directed graphs, which further leads to some similarities. Although it is often not possible to compare them in general, we achieved a good comparison between the width measures within this framework. The equality of directed path-width and directed tree-width on directed co-graphs generalizes the known results for undirected co-graphs of Bodlaender and Möhring.

在本文中，我们考虑有向图宽度度量的是递归定义的有向图的有向路径宽度，有向树宽度，有向反馈顶点集数，有向反馈弧集数，循环秩，DAG深度，DAG宽度和凯利宽度。尽管这些宽度测度的最小化问题通常是NP难的，但我们证明了在限于有向共形图的情况下，除了凯利宽度以外，所有这些参数都可以在线性时间内计算出来。作为重要的组合工具，我们展示了如何针对两个有向图的不相交并集，阶数组成，有向联盟和级数组成计算这些度量，这进一步导致了一些相似之处。尽管通常不可能通常进行比较，但是我们在此框架内的宽度度量之间实现了很好的比较。