Topics in structural graph theory /edited by Lowell W. Beineke, Robin J. Wilson.
- New York : Cambridge University Press, (c)2013.
- 1 online resource (xiv, 327 pages) : illustrations.
- Encyclopedia of mathematics and its applications ; 147 .
Includes bibliographies and index.
Preliminaries / Menger's theorem / Maximally connected graphs / Minimal connectivity / Contractions of k-connected graphs / Connectivity and cycles / H-linked graphs / Tree-width and graph minors / Toughness and binding numbers / Graph fragmentability / The phase transition in random graphs / Network reliability and synthesis / Connectivity algorithms / Using graphs to find the best block designs / Lowell W. Beineke and Robin J. Wilson -- Ortrud O. Oellermann -- Dirk Meierling and Lutz Volkmann -- Matthias Kriesell -- Kiyoshi Ando -- R.J. Faudree -- Michael Ferrara and Ronald J. Gould -- Dieter Rautenbach and Bruce Reed -- Ian Anderson -- Keith Edwards and Graham Farr -- Béla Bollobás and Oliver Riordan -- F.T. Boesch, A. Satyanarayana and C.L. Suffel -- Abdol-Hossein Esfahanian -- R.A. Bailey and Peter J. Cameron.
"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"--