Topics in structural graph theory
By: edited by Lowell W. Beineke, Robin J. Wilson
Series: Encyclopedia of mathematics and its applications -- 147
Publisher: Cambridge University Press
Published: 2013
Place of publication: New York
Language: eng
Number of pages: 327
ISBN-13: 9780521802314
Subjects: MATHEMATICS / Discrete Mathematics; Graph theory; Data processing
Description: "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"--
Table of contents: title: Machine generated contents note: Foreword Ortrud R. Oellermann; Preliminaries Lowell W. Beineke and Robin J. Wilson; 1. Menger's theorem Ortrud O. Oellermann; 2. Maximal connectivity 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 number Ian Anderson; 9. Graph fragmentability Keith Edwards and Graham Farr; 10. The phase transition in random graphs Bela 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.