developed by Paul Seymour and Neil Robertson and followers), which certainly now deserves a monographic treatment of its own. Summing up: Recommended. Lower-division undergraduate through professional collections.
CHOICE
This book is a follow-on to the authors' 1976 text, Graphs with Applications. What began as a revision has evolved into a modern, first-class, graduate-level textbook reflecting changes in the discipline over the past thirty years... This text hits the mark by appearing in Springer’s Graduate Texts in Mathematics series, as it is a very rigorous treatment, compactly presented, with an assumption of a very complete undergraduate preparation in all of the standard topics. While the book could ably serve as a reference for many of the most important topics in graph theory, it fulfills the promise of being an effective textbook. The plentiful exercises in each subsection are divided into two groups, with the second group deemed "more challenging". Any exercises necessary for a complete understanding of the text have also been marked as such. There is plenty here to keep a graduate student busy, and any student would learn much in tackling a selection of the exercises... Not only is the content of this book exceptional, so too is its production. The high quality of its manufacture, the crisp and detailed illustrations, and the uncluttered design complement the attention to the typography and layout. Even in simple black and white with line art, it is a beautiful book.
SIAM Book Reviews
"A text which is designed to be usable both for a basic graph theory course … but also to be usable as an introduction to research in graph theory, by including more advanced topics in each chapter. There are a large number of exercises in the book … . The text contains drawings of many standard interesting graphs, which are listed at the end." (David B. Penman, Zentralblatt MATH, Vol. 1134 (12), 2008)
MathSciNet Reviews
"The present volume is intended to serve as a text for "advanced undergraduate and beginning graduate students in mathematics and computer science" (p. viii). It is well suited for this purpose. The writing is fully accessible to the stated groups of students, and indeed is not merely readable but is engaging… Even a complete listing of the chapters does not fully convey the breadth of this book… For researchers in graph theory, this book offers features which parallel the first Bondy and Murty book: it provides well-chosen terminology and notation, a multitude of especially interesting graphs, and a substantial unsolved problems section…One-hundred unsolved problems are listed in Appendix A, a treasure trove of problems worthy of study… (In short) this rewrite of a classic in graph theory stands a good chance of becoming a classic itself."
"The present volume is intended to serve as a text for ‘advanced undergraduate and beginning graduate students in mathematics and computer science’ … . The writing is fully accessible to the stated groups of students, and indeed is not merely readable but is engaging. The book has many exercise sets, each containing problems … ." (Arthur M. Hobbs, Mathematical Reviews, Issue 2009 C)
"A couple of fantastic features: Proof techniques: I love these nutshelled essences highlighted in bordered frames. They look like pictures on the wall and grab the view of the reader. Exercises: Their style, depth and logic remind me of Lovász’ classical exercise book. Also the fact that the name of the author is bracketed after the exercise…Figures: Extremely precise and high-tech…The book contains very recent results and ideas. It is clearly an up-to-date collection of fundamental results of graph theory…All-in-all, it is a marvelous book." (János Barát, Acta Scientiarum Mathematicarum, Vol. 75, 2009)
