On Clique Growth in Products of Directed Graphs

Abstract.

 The Sperner product of the digraphs and is the digraph whose vertex set is the Cartesian product of the vertex set of the two, while there is an arc in pointing from to if either or both of the relations and hold. We study the growth of the largest transitively oriented clique in the Sperner powers of a fixed graph G and derive the first non-trivial upper bounds on the Sperner capacity of arbitrary digraphs.