Review from Acta Scientiarum Mathematicarum
Graph theory is gaining fast growing importance in college and university
education. Its applications in computer science, economics, optimization
make graph theory an obligatory part in syllabuses of electrical engineering,
operations research, economics majors. Following this trend the number of
graph theory textbooks on the market is also fast growing. Reinhard Diestel's
work is certainly much more than just a small supplement to the previous
works. It is an outstanding attempt to give a firm basis for graph theoretical
studies and to give a glimpse of the most current techniques. In order to
do that the author covers topics that are not traditional in earlier textbooks
or not even covered in any of them.
The book consists of twelve chapters: The basics, Matching, Connectivity,
Planar graphs, Colouring, Flows, Substructures in sparse graphs, Ramsey
theory for graphs, Hamiltonian cycles, Random graphs, Minors, trees, and
We should point out that some chapters are completely new in the literature.
For example, Szemerédi's regularity lemma and Seymour-Robertson theory
are not carefully thought about so far in textbooks. Some classical topics
also give pleasant surprises for the reader. In addition to the five color
theorem, Thomassen's extremely simple proof that each simple planar graph
is 5-choosable is also presented.
The presentation is very condensed. This is achieved by careful thinking
to choose the right proof to present. This is a result of great teaching
experience and extensive discussion with fellow researchers over several
years. An earlier German version preceded the book.
The presentation of the book is attractive. Notation and cross references
(between different chapters) are listed in the margin. At first look this
gives a strange appearance for the book but the careful readers (especially
the novice readers) obtain considerable extra information by following the
cross references. Each chapter ends with notes, containing very helpful
historical notes and references. At the end of the book an Index and a Symbol
index help the reader to find the necessary pointers. There is no complete
list of references in the book (the references of the book are given at
the end of chapters, as mentioned earlier).
Each chapter is supplemented with exercises. The hardness of the exercises
is marked by - and + signs. No solutions are given although when the author
felt it necessary an immediate hint follows the exercise.
Some of the chapters of the book can be used in undergraduate courses. But
the major use of the book will be at graduate courses and graph theory seminars.
We highly recommend this book for graph theorists, graduate students in
graph theory, and anyone who needs graph theoretical methods in his/her
work. This book cannot be substituted with any other book on the present
textbook market. The referee's opinion is that the present book has the
chance to become the standard textbook for graph theory.
Peter Hajnal (Szeged)
Acta Scientiarum Mathematicarum
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