A duality theorem for graph embeddings

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 K,L in orientable surfaces S, such that S are branched covers of S and the restrictions of the branched coverings to K,L 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.

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