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Topics in Topological Graph Theory by Jonathan L. Gross, Robin J. Wilson, Lowell W. Beineke

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3Distribution of embeddings

JONATHAN L. GROSS

1. Introduction

2. Enumerating embeddings by surface type

3. Total embedding distributions

4. Congruence classes

5. The unimodality problem

6. Average genus

7. Stratification of embeddings

References

        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.

1. Introduction

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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