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Topics in Topological Graph Theory

$160.00 (R)

Part of Encyclopedia of Mathematics and its Applications

Jonathan L. Gross, Thomas W. Tucker, Lowell W. Beineke, Robin J. Wilson, Jianer Chen, Yuanqiu Huang, Bojan Mohar, R. Bruce Richter, Joan P. Hutchinson, G. Salazar, Tomaž Pisanski, Arjana Žitnik, Jin Ho Kwak, Jaeun Lee, Jozef Širáň, Arthur T. White, M. J. Grannell, T. S. Griggs, Mark E. Watkins, Dan Archdeacon
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  • Date Published: August 2009
  • availability: Available
  • format: Hardback
  • isbn: 9780521802307

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About the Authors
  • 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.

    • Good and timely coverage of the rapidly expanding area of topological graph theory written by world leaders in the field
    • Covers the main parts of the subject: topology of surfaces and graph theory
    • Extensive introductory chapter introduces background material
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    Product details

    • Date Published: August 2009
    • format: Hardback
    • isbn: 9780521802307
    • length: 366 pages
    • dimensions: 241 x 165 x 27 mm
    • weight: 0.7kg
    • contains: 7 b/w illus. 15 tables
    • availability: Available
  • Table of 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.

  • Editors

    Lowell W. Beineke, Purdue University, Indiana
    Lowell W. Beineke is Schrey Professor of Mathematics at Indiana University–Purdue University Fort Wayne, where he has been since receiving his Ph.D. from the University of Michigan under the guidance of Frank Harary. His graph theory interests are broad, and include topological graph theory, line graphs, tournaments, decompositions and vulnerability. With Robin Wilson he edited Selected Topics in Graph Theory (3 volumes), Applications of Graph Theory, Graph Connections and Topics in Algebraic Graph Theory. Until recently he was editor of the College Mathematics Journal.

    Robin J. Wilson, The Open University, Milton Keynes
    Robin J. Wilson is Professor of Pure Mathematics at the Open University, UK, and Emeritus Professor of Geometry at Gresham College, London. After graduating from Oxford, he received his Ph.D. in number theory from the University of Pennsylvania. He has written and edited many books on graph theory and the history of mathematics, including Introduction to Graph Theory and Four Colours Suffice, and his research interests include graph colourings and the history of combinatorics, and he has Erdős number 1. He has won a Lester Ford Award and a George Pólya Award from the MAA for his expository writing.

    Consultant Editors

    Jonathan L. Gross, Columbia University, New York
    Jonathan L. Gross is Professor of Computer Science at Columbia University. His mathematical work in topology and graph theory have earned him an Alfred P. Sloan Fellowship, an IBM Postdoctoral Fellowship, and numerous research grants. With Thomas Tucker, he wrote Topological Graph Theory and several fundamental pioneering papers on voltage graphs and on enumerative methods. He has written and edited eight books on graph theory and combinatorics, seven books on computer programming topics, and one book on cultural sociometry.

    Thomas W. Tucker, Colgate University, New York
    Thomas W. Tucker is the Charles Hetherington Professor of Mathematics at Colgate University, where he has been since 1973, after a PhD in 3-manifolds from Dartmouth in 1971 and a postdoc at Princeton (where his father A. W. Tucker was chairman and John Nash's thesis advisor). He is co-author (with Jonathan Gross) of Topological Graph Theory. His early publications were on non-compact 3-manifolds, then topological graph theory, but his recent work is mostly algebraic, especially distinguishability and the group-theoretic structure of symmetric maps.

    Contributors

    Jonathan L. Gross, Thomas W. Tucker, Lowell W. Beineke, Robin J. Wilson, Jianer Chen, Yuanqiu Huang, Bojan Mohar, R. Bruce Richter, Joan P. Hutchinson, G. Salazar, Tomaž Pisanski, Arjana Žitnik, Jin Ho Kwak, Jaeun Lee, Jozef Širáň, Arthur T. White, M. J. Grannell, T. S. Griggs, Mark E. Watkins, Dan Archdeacon

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