Graphs, networks and algorithms Dieter Jungnickel. Algorithms and computation in mathematics 5.

From the reviews of the German edition:"Combinatorial optimization, along with graph algorithms and complexity theory is booming. This book treats the most prominent problems which are polynomially solvable. The Traveling Salesman Problem is discussed as a paradigm of an NP-complete problem. The text is well written, most exercises are quite enlightening and the hints are clear. Algorithms are described very thoroughly. The list of references is impressive and gives good guidance for further reading. The book can be recommended to beginners as an introductory text as well as for research and industry as a reference. "(OPTIMA)In this corrected 2nd printing of the first edition the author has made some small modifications: some minor mistakes were corrected and updates to the bibliography provided.

From reviews: “.... 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) “This book has been a pleasure to read and review. Its title is brief and self-explanatory, and the book has been well-produced and designed for both reference and systematic use. .... Firstly, it is an extremely clear text; ... Secondly, the author is not ashamed to introduce practice and illustrations, so that this is not a “dry-as-dust” text in esoteric mathematics. Algorithms are presented in pseudocode, and their workings are thoroughly discussed. It is a comprehensive book. ... Therefore, if you have the slightest interest in the algorithms for graphs and networks, or in the theory of such models, then Jungnickel has produced a book that you ought to have available for reference.” (David K. Smith, University of Exeter, Journal of the Operational Research Society, 50 (1999) “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.” (Peter B. Gibbons, Auckland, Zentralblatt für Mathematik 1061, 2005) From the reviews of the second edition: "This book ... beginning from the very basic definitions of graph theory, quickly building a catalog of theorems, and ending with a complex suite of algorithms on graphs and networks. ... At the end is a collection of NP-complete problems and an extensive bibliography. This text is suitable for graduate courses in combinatorics and graph theory, as well as for independent study and research by students, mathematicians, and professionals. It is a welcome addition to the library of choices of textbooks for these subjects." (William Fahle, SIGACT News, Vol. 36 (4), 2005) From the reviews of the third edition: "The third edition of this standard textbook contains further new material on graphical codes and their decoding, and many additional exercises. ... The focus on algorithmic issues motivates challenging questions, and connects the presentation to many real applications. ... appropriate for computer science and engineering students, in addition to students of mathematics. The diversity of applications represented is a real strength of the text. ... provides connections to other areas of mathematics, and applications, that serve to motivate students. The book is highly recommended." (Charles J. Colbourn, Zentralblatt MATH, Vol. 1126 (3), 2008)