2. Enumerating embeddings by surface type

3. Total embedding distributions

7. Stratification of embeddings

*The principal genus distribution problem is to count the number of cellular embeddings of a given graph. Complete distributions have been obtained for a few basic families of graphs. Various properties of genus distributions and of related invariants are examined, especially the properties of the average genus*.

A ubiquitous question in topological graph theory is whether a given graph can be embedded in a given surface, a question that readily extends to the problem of counting ...

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