Topics in Structural Graph Theory

No other book covers such a wide scope of this aspect of graph theory.

Lowell W. Beineke (Edited by), Robin J. Wilson (Edited by), Ortrud R. Oellermann (Consultant editor)

9780521802314, Cambridge University Press

Hardback, published 8 November 2012

342 pages, 60 b/w illus.
24 x 16 x 2.2 cm, 0.67 kg

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.

Subject Areas: Combinatorics & graph theory [PBV], Discrete mathematics [PBD], Coding theory & cryptology [GPJ]