We introduce a new digraph width measure called directed branch-width. To do this, we generalize a characterization of graph classes of bounded tree-width in terms of their line graphs to digraphs. Although we prove that underlying branch-width cannot be bounded in terms of our new measure, we show that directed branch-width is a natural generalization of its undirected counterpart and indeed the two invariants can be related via the operation of identifying pairs of sources or pairs of sinks. Leveraging these operations and the relationship to underlying tree-width allows us to extend a range of algorithmic results from directed graphs with bounded underlying treewidth to the larger class of digraphs having bounded directed branch-width.

翻译：我们引入一种新的有向图宽度度量——有向分支宽度。为此，我们将树宽有界图类基于其线图的刻画推广至有向图。虽然我们证明基础分支宽度无法被新度量所界定，但研究表明有向分支宽度是其无向版本的自然推广，且这两个不变量可通过识别源点对或汇点对的运算建立关联。借助这些运算及其与底层树宽的关系，我们得以将一系列从具有有界底层树宽的有向图到更大图类——即具有有界有向分支宽度的有向图——的算法结果进行扩展。