The use of topological ideas to explore various aspects of graph theory, and vice versa, is a fruitful area of research. There are links with other areas of mathematics, such as design theory and geometry, and increasingly with such areas as computer networks where symmetry is an important feature. Other books cover portions of the material here, but there are no other books with such a wide scope. This book contains fifteen expository chapters written by acknowledged international experts in the field. Their well-written contributions have been carefully edited to enhance readability and to standardize the chapter structure, terminology and notation throughout the book. To help the reader, there is an extensive introductory chapter that covers the basic background material in graph theory and the topology of surfaces. Each chapter concludes with an extensive list of references.

- Cover
- Title Page
- Copyright Page
- Contents
- Foreword
- Preface
- Introduction
- 1 Embedding Graphs on Surfaces
- 2 Maximum Genus
- 3 Distribution of Embeddings
- 4 Algorithms and Obstructions for Embeddings
- 5 Graph Minors: Generalizing Kuratowskiâ€™s Theorem
- 6 Colouring Graphs on Surfaces
- 7 Crossing Numbers
- 8 Representing Graphs and Maps
- 9. Enumerating Coverings
- 10 Symmetric Maps
- 11. The Genus of a Group
- 12. Embeddings and Geometries
- 13.Embeddings and Designs
- 14. Infinite Graphs and Planar Maps
- 15 Open Problems
- Notes on Contributors
- Index