Planar graphs on the projective plane Original Research Article

It is shown that embeddings of planar graphs in the projective plane have very specific structure. By exhibiting this structure we indirectly characterize graphs on the projective plane whose dual graphs are planar. Whitneyʹs Theorem about 2-switching equivalence of planar embeddings is generalized: Any two embeddings of a planar graph in the projective plane can be obtained from each other by means of simple local reembeddings, very similar to Whitneyʹs switchings.