The Dimensional Collective are an anomalous faction, so I am not quite able to describe their "Territory" in a way that would make sense for the map.
I suppose the closest approximation would be a cyan region at the top of the Red (Forbidden?) Galaxy. Preferably near the Hyper-FTL Nodes.
Also add a smaller, sky-blue (or otherwise darker cyan) color region in a relatively unpopulated sector of the leftmost galaxy, and add the "Theta-Icoveo Rift" there. Those are the "Fallen Rogues" Collective, a rebel branch of the Dimensional Collective led by the infamous "Alpha-Alpha."