Topics in Structural Graph Theory Encyclopedia of Mathematics and its Applications Series

The rapidly expanding area of structural graph theory uses ideas of connectivity to explore various aspects of graph theory and vice versa. It has links with other areas of mathematics, such as design theory and is increasingly used in such areas as computer networks where connectivity algorithms are an important feature. Although other books cover parts of this material, none has a similarly wide scope. Ortrud R. Oellermann (Winnipeg), internationally recognised for her substantial contributions to structural graph theory, acted as academic consultant for this volume, helping shape its coverage of key topics. The result is a collection of thirteen expository chapters, each written by acknowledged experts. These contributions have been carefully edited to enhance readability and to standardise the chapter structure, terminology and notation throughout. An introductory chapter details the background material in graph theory and network flows and each chapter concludes with an extensive list of references.

Foreword Ortrud R. Oellermann; Preface Lowell W. Beineke and Robin J. Wilson; Preliminaries Lowell W. Beineke and Robin J. Wilson; 1. Menger's theorem Ortrud R. Oellermann; 2. Maximally connected graphs Dirk Meierling and Lutz Volkmann; 3. Minimal connectivity Matthias Kriesell; 4. Contractions of k-connected graphs Kiyoshi Ando; 5. Connectivity and cycles R. J. Faudree; 6. H-linked graphs Michael Ferrara and Ronald J. Gould; 7. Tree-width and graph minors Dieter Rautenbach and Bruce Reed; 8. Toughness and binding numbers Ian Anderson; 9. Graph fragmentability Keith Edwards and Graham Farr; 10. The phase transition in random graphs Béla Bollobás and Oliver Riordan; 11. Network reliability and synthesis F. T. Boesch, A. Satyanarayana and C. L. Suffel; 12. Connectivity algorithms Abdol-Hossein Esfahanian; 13. Using graphs to find the best block designs R. A. Bailey and Peter J. Cameron; Notes on contributors; Index.

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, Topics in Algebraic Graph Theory and Topics in Topological Graph Theory. Until recently he was editor of the College Mathematics Journal.
Robin J. Wilson is Emeritus Professor of Pure Mathematics at the Open University, UK. He was recently Gresham Professor of Geometry, London and a Fellow in Mathematics at Keble College, University of Oxford, and now teaches at Pembroke College, Oxford. He graduated in mathematics from the University of Oxford and 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, Four Colours Suffice and Lewis Carroll in Numberland and his research interests include graph colourings and the history of combinatorics. He is currently President of the British Society for the History of Mathematics.