Digraphs: Theory, Algorithms and Applications - Hardcover

Bang-Jensen, Jorgen; Gutin, Gregory

Hardcover

ISBN 10: 1852332689 ISBN 13: 9781852332686

Publisher: Springer Verlag, 2000

Synopsis

The study of directed graphs has developed enormously over recent decades, yet no book covers more than a tiny fraction of the results from more than 3000 research articles on the topic. Digraphs is the first book to present a unified and comprehensive survey of the subject. In addition to covering the theoretical aspects, including detailed proofs of many important results, the authors present a number of algorithms and applications. The applications of digraphs and their generalizations include among other things recent developments in the Travelling Salesman Problem, genetics and network connectivity. More than 700 exercises and 180 figures will help readers to study the topic while open problems and conjectures will inspire further research.
This book will be essential reading and reference for all graduate students, researchers and professionals in mathematics, operational research, computer science and other areas who are interested in graph theory and its applications.

About this title

From the Back Cover

The theory of directed graphs has developed enormously over recent decades, yet this book (first published in 2000) remains the only book to cover more than a small fraction of the results. New research in the field has made a second edition a necessity.

Substantially revised, reorganised and updated, the book now comprises eighteen chapters, carefully arranged in a straightforward and logical manner, with many new results and open problems.

As well as covering the theoretical aspects of the subject, with detailed proofs of many important results, the authors present a number of algorithms, and whole chapters are devoted to topics such as branchings, feedback arc and vertex sets, connectivity augmentations, sparse subdigraphs with prescribed connectivity, and also packing, covering and decompositions of digraphs. Throughout the book, there is a strong focus on applications which include quantum mechanics, bioinformatics, embedded computing, and the travelling salesman problem.

Detailed indices and topic-oriented chapters ease navigation, and more than 650 exercises, 170 figures and 150 open problems are included to help immerse the reader in all aspects of the subject.

Digraphs is an essential, comprehensive reference for undergraduate and graduate students, and researchers in mathematics, operations research and computer science. It will also prove invaluable to specialists in related areas, such as meteorology, physics and computational biology.

Jørgen Bang-Jensen is a Professor in the Department of Mathematics and Computer Science at the University of Southern Denmark, Odense, Denmark.

Gregory Gutin is Professor of Computer Science at Royal Holloway College, University of London, UK.

Review

From the reviews:

"Digraphs (directed graphs) are a long-standing and important field of graph theory. Nevertheless, this is the first comprehensive monograph devoted to the subject. As a handbook, it addresses various groups of readers (students as well as researchers, and from various areas of applications). Throughout, because of their importance for applications, emphasis is on algorithms (in form of constructive proofs whenever possible). ... a valuable and indispensable reference for many years to come. Readers and users will be thankful!" (P. Schmitt, Monatshefte für Mathematik, Vol. 141 (1), 2004)

From the reviews of the second edition:

"This is a very comprehensive volume on directed graphs and related topics. ... an excellent reference. ... the book will be useful not just for researchers focusing on digraphs, but also for everyone ... . an extensive list of conjectures and open questions is included in every chapter. These are typically very well presented and easy to understand." (Miklós Bóna, MAA Online, February, 2009)

“The first edition of this book was published in 2000 ... . The area has continued to develop and this reorganized and updated edition contains an additional six chapters ... . there is a strong emphasis on algorithms, and constructive proofs are given whenever possible. There are more than 650 exercises and 150 open problems and conjectures. ... the bibliography contains 934 items and the author index contains 740 names. This book would be a valuable resource for anyone interested in digraphs and their applications.” (J. W. Moon, Zentralblatt MATH, Vol. 1170, 2009)

Edition details

• Publisher: Springer Verlag
• Publication date: 2000
• ISBN 10: 1852332689
• ISBN 13: 9781852332686
• Binding: Hardcover
• Language: English