components which each contain at most the vertices of the original. As is built from two layers of opposed dipaths, each separator may consist of up to 2 dipaths, for a total of up to 6 dipaths over all of the separators. Let be this set of dipaths. The proof that such separators can always be found is related to the Planar Separator Theorem of Lipton and Tarjan, and these separators can be located in linear time.

For each , the directed nature of provides for a natural indexing of