By C. Berge, D. Ray-Chaudhuri
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Extra resources for Hypergraph Seminar
Whereas the topological theory of covering spaces describes an existential relationship between the domain and the codomain of a mapping, the theory of voltage graphs, due to Gross  and Gross and Tucker , provides a combinatorial tool for constructing graphs and graph embeddings. In voltage graph theory, the many specialized forms of combinatorial current graph originating with Gustin and augmented by Ringel and Youngs (see ) are all unified, so that the Ringel–Youngs embeddings are readily understood as the duals of coverings of voltage graphs (see  and ).
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Gross and Thomas W. Tucker with a variety of standard enumerative methods. Such inventories are the topic of Chapter 3. In recent years, Kwak and Lee have led in the application of voltage graph methods for enumerating graph coverings, and Chapter 9 provides an account of this active branch of topological graph theory. Combinatorial methods predominated in the older, complementary programme of research launched by Tutte ,  into the counting of maps on a given surface. Jackson and Visentin  have provided a complete listing of the maps with a small number of edges.