Shallow grates
This note gives a construction for a family of weak grates; that is, acyclic digraphs of logarithmic depth with this property: A superlinear number of pairs of vertices remain connected after removing any sufficiently small linear sized vertex set. The construction is based on one by Schnitger for acyclic digraphs with a similar property. Schnitger's graphs are modified by replacing vertices and edges by appropriate vertex sets and edge sets. The construction easily generalizes to digraphs of arbitrary depth.
scientific article; zbMATH DE number 501199