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

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1Embedding graphs on surfaces

JONATHAN L. GROSS and THOMAS W. TUCKER

1. Introduction

2. Graphs and surfaces

3. Embeddings

4. Rotation systems

5. Covering spaces and voltage graphs

6. Enumeration

7. Algorithms

8. Graph minors

References

        In this first chapter, we review the basic ideas of topological graph theory. We describe the principal early theme of constructing embeddings, and we then survey the launching of the dominant programmatic themes of the present era, which are presented in greater detail individually in subsequent chapters.

1. Introduction

By the late 19th century, the work of Heawood [16] and Heffter [17] had expanded the study of graph drawings beyond the confines of the plane to surfaces of higher order. Over the next ...

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