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.

from 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 1061, 2005)

the Third Edition Of This Standard Textbook Contains Additional Material: Two New Application Sections (on Graphical Codes And Their Decoding) And About Two Dozen Further Exercises (with Solutions, As Throughout The Text). Moreover, Recent Developments Have Been Discussed And Referenced, In Particular For The Travelling Salesman Problem. The Presentation Has Been Improved In Many Places (for Instance, In The Chapters On Shortest Paths And On Colorings), And A Number Of Proofs Have Been Reorganized, Making Them More Precise Or More Transparent.

From the reviews of the 2nd edition The substantial development effort of this text 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. Zentralblatt für Mathematik 2005 The third edition of this standard textbook contains additional material: two new application sections (on graphical codes and their decoding) and about two dozen further exercises (with solutions, as throughout the text). Moreover, recent developments have been discussed and referenced, in particular for the travelling salesman problem. The presentation has been improved in many places (for instance, in the chapters on shortest paths and on colorings), and a number of proofs have been reorganized, making them more precise or more transparent. Front Matter....Pages I-XX Basic Graph Theory....Pages 1-33 Algorithms and Complexity....Pages 35-63 Shortest Paths....Pages 65-102 Spanning Trees....Pages 103-134 The Greedy Algorithm....Pages 135-161 Flows....Pages 163-218 Combinatorial Applications....Pages 219-249 Connectivity and Depth First Search....Pages 251-273 Colorings....Pages 275-293 Circulations....Pages 295-358 The Network Simplex Algorithm....Pages 359-378 Synthesis of Networks....Pages 379-403 Matchings....Pages 405-439 Weighted Matchings....Pages 441-479 A Hard Problem: The TSP....Pages 481-526 Back Matter....Pages 527-675 "The third edition of this standard textbook contains additional material: two new application sections (on graphical codes and their decoding) and about two dozen further exercises (with solutions, as throughout the text). Moreover, recent developments have been discussed and referenced, in particular for the travelling salesman problem. The presentation has been improved in many places (for instance, in the chapters on shortest paths and on colorings), and a number of proofs have been reorganized, making them more precise or more transparent."--Jacket