- Series: Springer Monographs in Mathematics
- Paperback: 776 pages
- Publisher: Springer (August 5, 2002)
- Language: English
- ISBN-10: 1852336110
- ISBN-13: 978-1852336110
- Product Dimensions: 6.1 x 1.5 x 9.2 inches
- Shipping Weight: 2.4 pounds
- Average Customer Review: 3.9 out of 5 stars See all reviews (2 customer reviews)
- Amazon Best Sellers Rank: #4,641,522 in Books (See Top 100 in Books)
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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)
"“This is a very comprehensive volume on directed graphs and related topics… [an] impressive, well-conceived, and well-written book...it is an excellent reference…[useful] for a series of seminars, where each student would be responsible for presenting a part of the material, including proofs that are in the book and proofs that are not in the book…unlike in a large number of research monographs, the authors do an excellent job putting their topic into context. Hence the book will be useful not just for researchers focusing on digraphs, but also for everyone else for whom digraphs are tools, and not goals…
Last, but not least, an extensive list of conjectures and open questions is included in every chapter. These are typically very well presented and easy to understand. I am not taking a big risk when I predict that with the help of books like this, the area will continue to progress at a fast pace.”(Miklós Bóna, MAA Online )
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.--This text refers to the Hardcover edition.
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Top Customer Reviews
The text strives to accomplish the following objectives:
1. To give a great deal of information on both results and proof techniques for specialists in graph theory. No other book covers even 10\% of material provided in Digraphs, and thus before this monograph has been published even specialists in graph theory very often needed to search for a specific result or proof technique through the ocean of literature on digraphs. Now the situation has drastically improved.
2. To introduce researchers and practitioners from various other fields in mathematics, computer science, operations research, biology, etc. to basic and more advanced results in digraph theory and algorithms and some carefully selected applications. It offers much more than merely a pure bibliography and provides the ideal starting point for any researcher who needs to become familiar either with theory oriented aspects of this interesting area or with some application in a relatively short time.
3. To provide enough material for intermediate and final year BSc or MSc courses for students in mathematics, computer science and operations research. The large number of exercises (more than 700) of various difficulty is of great help to instructors and lecturers. The applications provided in the book will help to provide enough motivation for the students to study digraph theory and algorithms.
4. To provide a large variety of topics for final year student projects in mathematics, computer science, operations research and other fields. The monograph can be used as a source for the projects because because several areas of digraph theory are covered there in real depth and they vary from relatively simple to reasonably complicated ones.
To summarize, I'd like to notice that the monograph is aimed to a wide range of readers including specialists in mathematics, operations research, computer science, biology, etc. as well as students of second year and higher.
Boris Goldengorin, Department of Econometrics and Operations Research, University of Groningen, The Netherlands