Planar graphs have been a major topic of interest in graph theory, thanks to the four-color problem. The importance of understanding graphs embedded on surfaces became clear after the groundbreaking work of Robertson and Seymour in connection with their work on Wagner's conjecture. I will address the following questionIs there a complete set of operations that can explain different embeddings of a nonplanar graph on the projective plane? This is joint work with John Maharry, Neil Robertson and Daniel Slilaty.
