Extremal Digraph Results for Topological Complete Subgraphs

We determine, to within a constant factor, the maximum size of a digraph that does not contain a topological complete digraphDKpof orderp. Lett1(p) be defined for positivepby denotes a digraph. We show that o obtain results for containing topological tournaments, and a Turلn-type result for containing a topological transitive tournament and a transitive tournament.