Topics in Topological Graph Theory

Jonathan L. Gross; Thomas W. Tucker

doi:10.1017/CBO9781139087223

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.

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Contents

Frontmatter
pp i-viii
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Contents
pp ix-xiv
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Foreword
pp xv-xvi
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Preface
pp xvii-xviii
- By Lowell W. Beineke, Robin J. Wilson
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Introduction
pp 1-17
- By Lowell W. Beineke, Purdue University, Indiana , Robin J. Wilson, The Open University, Milton Keynes
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1 - Embedding graphs on surfaces
pp 18-33
- By Jonathan L. Gross, Columbia University, Thomas W. Tucker, Colgate University
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2 - Maximum genus
pp 34-44
- By Jianer Chen, New York University, Yuanqiu Huang, Mathematics at the Hunan Normal University
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3 - Distribution of embeddings
pp 45-61
- By Jonathan L. Gross, Columbia University, Thomas W. Tucker, Colgate University
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4 - Algorithms and obstructions for embeddings
pp 62-80
- By Bojan Mohar, Simon Fraser University, Canada, and at the University of Ljubljana, Slovenia
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5 - Graph minors: generalizing Kuratowski's theorem
pp 81-110
- By R. Bruce Richter, University of Waterloo
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6 - Colouring graphs on surfaces
pp 111-132
- By Joan P. Hutchinson, University of Pennsylvania
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7 - Crossing numbers
pp 133-150
- By R. Bruce Richter, University of Waterloo, G. Salazar, Institute of Physics at the Universidad Autónoma de San Luis Potosi
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8 - Representing graphs and maps
pp 151-180
- By Tomaž Pisanski, University of Ljubljana, Slovenia, Arjana Žitnik, University of Ljubljana, Slovenia
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9 - Enumerating coverings
pp 181-198
- By Jin Ho Kwak, University of Science and Technology in Korea, Jaeun Lee, Yeungnam University in Korea
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10 - Symmetric maps
pp 199-224
- By Jozef Širáň, University of Technology, Slovakia, Thomas W. Tucker, Colgate University
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11 - The genus of a group
pp 225-244
- By Thomas W. Tucker, Colgate University
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12 - Embeddings and geometries
pp 245-267
- By Arthur T. White, Western Michigan University
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13 - Embeddings and designs
pp 268-288
- By M. J. Grannell, University of Central Lancashire, T. S. Griggs, The Open University, UK
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14 - Infinite graphs and planar maps
pp 289-312
- By Mark E. Watkins, University of North Carolina
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15 - Open problems
pp 313-336
- By Dan Archdeacon, University of Vermont
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Notes on contributors
pp 337-340
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Index
pp 341-347
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Topics in Topological Graph Theory

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Contents

Frontmatter
pp i-viii

Contents
pp ix-xiv

Foreword
pp xv-xvi

Preface
pp xvii-xviii

Introduction
pp 1-17

1 - Embedding graphs on surfaces
pp 18-33

2 - Maximum genus
pp 34-44

3 - Distribution of embeddings
pp 45-61

4 - Algorithms and obstructions for embeddings
pp 62-80

5 - Graph minors: generalizing Kuratowski's theorem
pp 81-110

6 - Colouring graphs on surfaces
pp 111-132

7 - Crossing numbers
pp 133-150

8 - Representing graphs and maps
pp 151-180

9 - Enumerating coverings
pp 181-198

10 - Symmetric maps
pp 199-224

11 - The genus of a group
pp 225-244

12 - Embeddings and geometries
pp 245-267

13 - Embeddings and designs
pp 268-288

14 - Infinite graphs and planar maps
pp 289-312

15 - Open problems
pp 313-336

Notes on contributors
pp 337-340

Index
pp 341-347

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