On directed analogues of expander and hyperfinite graph sequences
Endre Cs\'oka, {\L}ukasz Grabowski
TL;DR
This paper introduces directed analogues of expander and hyperfinite graph sequences, called extender and hypershallow, and provides a probabilistic construction of non-hypershallow sequences, advancing understanding of directed graph properties.
Contribution
It defines new directed graph sequence classes and offers a probabilistic method to construct non-hypershallow sequences, expanding the theoretical framework.
Findings
Introduced extender and hypershallow graph sequences.
Provided a probabilistic construction of non-hypershallow sequences.
Extended the theory of graph sequences to directed acyclic graphs.
Abstract
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.
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