Abstract A long standing open problem in extremal graph theory is to describe all graphs that maximize the number of induced copies of a path on four vertices. The character of the problem changes in the setting of oriented graphs, and becomes more tractable. Here we resolve this problem in the setting of oriented graphs without transitive triangles.

中文翻译：

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有向路径的可归纳性

摘要 极值图论中一个长期存在的开放问题是描述所有在四个顶点上最大化路径的诱导副本数的图。问题的性质在有向图的设置中发生变化，变得更容易处理。在这里，我们在没有传递三角形的有向图的设置中解决了这个问题。