Digraphs: Theory, Algorithms and Applications

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Springer, Dec 17, 2008 - Mathematics - 798 pages
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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.

 

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Contents

Basic Terminology Notation and Results
1
Classes of Digraphs
31
Distances
87
Flows in Networks
127
Connectivity of Digraphs
191
Hamiltonian Longest and VertexCheapest Paths and Cycles
227
Restricted Hamiltonian Paths and Cycles
275
Paths and Cycles of Prescribed Lengths
307
Packings Coverings and Decompositions
505
Increasing Connectivity
553
Feedback Sets and Vertex Orderings
583
EdgeColoured Multigraphs
607
Applications of Digraphs and EdgeColoured Graphs
642
Algorithms and Their Complexity
695
References
721
Symbol Index
761

Branchings
339
Linkages in Digraphs
373
Orientations of Graphs and Digraphs
417
Sparse Subdigraphs with Prescribed Connectivity
479
Author Index
767
Subject Index
776
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