We introduce and study analogues of expander and hyperfinite graph sequences in the context of directed acyclic graphs, which we call ‘extender’ and ‘hypershallow’ graph sequences, respectively. Our main result is a probabilistic construction of non-hypershallow graph sequences.

中文翻译：

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关于扩展器和超有限图序列的有向类似物

我们在有向无环图的上下文中介绍和研究扩展器和超有限图序列的类似物，我们分别称之为“扩展器”和“超浅”图序列。我们的主要结果是非超浅图序列的概率构造。