Topics in Topological Graph Theory

Comprehensive and up-to-date coverage of topological graph theory.

Lowell W. Beineke (Edited by), Robin J. Wilson (Edited by), Jonathan L. Gross (Consultant editor), Thomas W. Tucker (Consultant editor)

9780521802307, Cambridge University Press

Hardback, published 9 July 2009

366 pages, 7 b/w illus. 15 tables
24.1 x 16.5 x 2.7 cm, 0.7 kg

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.

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 Širá? 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.

Subject Areas: Combinatorics & graph theory [PBV], Topology [PBP]