Reinhard Diestel

Graph Theory

Review from Bulletin of the Institute of Combinatorics and its Applications

This new volume, of 287 pages with 115 figures, is Number 173 in the series Graduate Texts in Mathematics, published by Springer-Verlag. The softcover version (ISBN 0-387-98211-6) is priced at US$29.95; the hardcover version (ISBN 0-387-98210-8) is priced at US$59.95. Complete details are available at:

An idea of the scope of the book is best given by a listing of the Chapter titles: Basics; Matching; Connectivity; Planar Graphs; Colouring; Flows; Substructures in Dense Graphs; Substructures in Sparse Graphs; Ramsey Theory for Graphs; Hamilton Cycles; Random Graphs; Minors, Trees, and Well-quasi-ordering. Clearly, the work would serve as an excellent text for a graduate course.

However, the book is written with a dual purpose; it is also meant to be usable in any serious introductory course in graph theory [in this reviewer's opinion, it succeeds very well in this bipartite aim]. Many of the standard results are proved in two or more independent ways; this gives the beginning student an example of rigorous and exacting proofs, but it also provides such a student with insight into various important methods of proof. Notable proofs include Gasparian's very new one-page proof of the perfect Graph Theorem, as well as Gallai's classical (but nearly forgotten) algorithmic proof of Menger's Theorem. The author has written an excellent preface outlining his aims, and the preface is well worth careful reading.

At the end of each chapter, the author has included a set of challenging and instructive problems; these add greatly to the value of the book. He has also included a short set of "Notes" in which he indicates some of the historical background of the concepts in the chapter; these make fascinating reading, and one wishes that they were even a bit longer.

The book has received a very enthusiastic reception, which it amply deserves. I was at the recent British Conference in London in July of 1997, and Springer sold, on the first day of the conference, all the copies that they had brought along; an extra shipment from Springer's stock was completely exhausted on the second day! So Springer brought in a third supply; it also rapidly disappeared.

The book is written with great care, and its "coefficient of lucidity" is high. Every reader will have his own favourite among the chapters; mine was the chapter on Planar Graphs, where I found the exposition particularly attractive. But the whole work is a masterly elucidation of modern graph theory, and an important contribution to the literature of the subject.

Bulletin of the Institute of Combinatorics and its Applications

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