Topics in Structural Graph Theory

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.

• 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.