Graphs, Networks and Algorithms, 4th Edition

Graphs, Networks and Algorithms (Algorithms and Computation in Mathematics)
From the reviews of the previous editions “…. The book is a first class textbook and seems to be indispensable for everybody who has to teach combinatorial optimization. It is very helpful for students, teachers, and researchers in this area. The author finds a striking synthesis of nice and interesting mathematical results and practical applications. … the author pays much attention to the inclusion of well-chosen exercises. The reader does not remain helpless; solutions or at least hints are given in the appendix. Except for some small basic mathematical and algorithmic knowledge the book is self-contained. …” K.Engel, Mathematical Reviews 2002 The substantial development effort of this text, involving multiple editions and trailing in the context of various workshops, university courses and seminar series, clearly shows through in this new edition with its clear writing, good organisation, comprehensive coverage of essential theory, and well-chosen applications. The proofs of important results and the representation of key algorithms in a Pascal-like notation allow this book to be used in a high-level undergraduate or low-level graduate course on graph theory, combinatorial optimization or computer science algorithms. The well-worked solutions to exercises are a real bonus for self study by students. The book is highly recommended. P .B. Gibbons, Zentralblatt für Mathematik 2005 Once again, the new edition has been thoroughly revised. In particular, some further material has been added: more on NP-completeness (especially on dominating sets), a section on the Gallai-Edmonds structure theory for matchings, and about a dozen additional exercises – as always, with solutions. Moreover, the section on the 1-factor theorem has been completely rewritten: it now presents a short direct proof for the more general Berge-Tutte formula. Several recent research developments are discussed and quite a few references have been added.

Table of Contents

Chapter 1: Basic Graph Theory
Chapter 2: Algorithms and Complexity
Chapter 3: Shortest Paths
Chapter 4: Spanning Trees
Chapter 5: The Greedy Algorithm
Chapter 6: Flows
Chapter 7: Combinatorial Applications
Chapter 8: Connectivity and Depth First Search
Chapter 9: Colorings
Chapter 10: Circulations
Chapter 11: The Network Simplex Algorithm
Chapter 12: Synthesis of Networks
Chapter 13: Matchings
Chapter 14: Weighted Matchings
Chapter 15: A Hard Problem: The TSP
Appendix A: Some NP-Complete Problems
Appendix B: Solutions
Appendix C: List of Symbols