Review from Bulletin of the Institute of Combinatorics and
This new volume, of 287 pages with 115 figures, is Number 173 in the
Graduate Texts in Mathematics, published by Springer-Verlag. The
version (ISBN 0-387-98211-6) is priced at US$29.95; the hardcover
(ISBN 0-387-98210-8) is priced at US$59.95. Complete details are
An idea of the scope of the book is best given by a listing of the
titles: Basics; Matching; Connectivity; Planar Graphs; Colouring;
Substructures in Dense Graphs; Substructures in Sparse Graphs; Ramsey
for Graphs; Hamilton Cycles; Random Graphs; Minors, Trees, and
Clearly, the work would serve as an excellent text for a graduate
However, the book is written with a dual purpose; it is also meant to
usable in any serious introductory course in graph theory [in this
opinion, it succeeds very well in this bipartite aim]. Many of the
results are proved in two or more independent ways; this gives the
student an example of rigorous and exacting proofs, but it also
such a student with insight into various important methods of proof.
proofs include Gasparian's very new one-page proof of the perfect Graph
Theorem, as well as Gallai's classical (but nearly forgotten)
proof of Menger's Theorem. The author has written an excellent preface
his aims, and the preface is well worth careful reading.
At the end of each chapter, the author has included a set of
and instructive problems; these add greatly to the value of the book.
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
The book has received a very enthusiastic reception, which it amply
I was at the recent British Conference in London in July of 1997, and
sold, on the first day of the conference, all the copies that they had
along; an extra shipment from Springer's stock was completely exhausted
on the second day! So Springer brought in a third supply; it also
The book is written with great care, and its "coefficient of lucidity"
is high. Every reader will have his own favourite among the chapters;
was the chapter on Planar Graphs, where I found the exposition
attractive. But the whole work is a masterly elucidation of modern
theory, and an important contribution to the literature of the subject.
Bulletin of the Institute of Combinatorics and its Applications
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