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. Under parameterizations by directed branch-width we obtain linear time algorithms for many problems, such as directed Hamilton path and Max-Cut, which are hard when parameterized by other known directed width measures. More generally, we obtain an algorithmic meta-theorem for the model-checking problem for a restricted variant of MSO_2-logic on classes of bounded directed branch-width.

中文翻译：

---

定向分支宽度：树宽的定向模拟

我们引入了一种新的有向图宽度度量，称为有向分支宽度。为此，我们根据线图将有界树宽的图类的特征概括为有向图。在有向分支宽度参数化下，我们获得了许多问题的线性时间算法，例如有向哈密顿路径和 Max-Cut，当通过其他已知的有向宽度度量参数化时，这些算法很难。更一般地，我们获得了模型检查问题的算法元定理，该模型检查问题是在有界有向分支宽度类上的 MSO_2 逻辑的受限变体。