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：我们引入了一种新的分界线宽度测量法,称为“直线分宽”。 为此,我们从直线图的角度对被捆绑的树形图类进行概括描述。虽然我们证明分界线不能以我们的新测量法进行约束,但我们表明,直线分界线是其非直线对应方的自然概括,事实上,通过对源或汇进行辨别,可以将两种异差联系起来。 利用这些操作和与底线树形的关系,我们可以将带边线的直线图所产生的一系列算法结果扩展至已绑定直线分界线的较大型的分界线。