A duality theorem for graph embeddings
Brad Jackson, T. D. Parsons, Tomaž Pisanski · Journal of Graph Theory · 1981
Abstract A generalized type of graph covering, called a “Wrapped quasicovering” (wqc) is defined. If K, L are graphs dually embedded in an orientable surface S, then we may lift these embeddings to embeddings of dual graphs K̃,L̃ in orientable surfaces S̃, such that S̃ are branched covers of S and the restrictions of the branched coverings to K̃,L̃ are wqc's of K, L. the theory is applied to obtain genus embeddings of composition graphs G[nK1] from embeddings of “quotient” graphs G.