Re-embedding of projective-planar graphs
Let G be a graph embedded in a surface \(F^ 2\). An embedding \(f: G\to F^ 2\) is called a re-embedding of G in \(F^ 2\) if f cannot extend to a self-homeomorphism \(h: F^ 2\to F^ 2\) with \(h| _ G=f\). In this paper, re-embeddings of 3-connected nonplanar graphs embedded in the projective plane are classified into five types with respect to how bridges for the boundary cycle of a face are re-embedded. This classification theorem, called Re-embedding Theorem, is used to show that 5-connected projective-planar graphs with a certain condition are uniquely and faithfully embeddable in the projective plane.
scientific article; zbMATH DE number 3985250