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Full Description
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.
Contents
Preface; Foreword Jonathan L. Gross and Thomas W. Tucker; Introduction Lowell W. Beineke and Robin J. Wilson; 1. Embedding graphs on surfaces Jonathan L. Gross and Thomas W. Tucker; 2. Maximum genus Jianer Chen and Yuanqiu Huang; 3. Distributions of embeddings Jonathan L. Gross; 4. Algorithms and obstructions for embeddings Bojan Mohar; 5. Graph minors: generalizing Kuratowski's theorem R. Bruce Richter; 6. Colouring graphs on surfaces Joan P. Hutchinson; 7. Crossing numbers R. Bruce Richter and G. Salazar; 8. Representing graphs and maps Tomaž Pisanski and Arjana Žitnik; 9. Enumerating coverings Jin Ho Kwak and Jaeun Lee; 10. Symmetric maps Jozef Širáň and Thomas W. Tucker; 11. The genus of a group Thomas W. Tucker; 12. Embeddings and geometries Arthur T. White; 13. Embeddings and designs M. J. Grannell and T. S. Griggs; 14. Infinite graphs and planar maps Mark E. Watkins; 15. Open problems Dan Archdeacon; Notes on contributors; Index of definitions.
