Modern Graph Theory (Graduate Texts in Mathematics) [Hardcover]

Bela Bollobas (Author)

Book Description

ISBN-10: 0387984917 | ISBN-13: 978-0387984919 | Publication Date: July 1, 1998 | Edition: 1

The time has now come when graph theory should be part of the education of every serious student of mathematics and computer science, both for its own sake and to enhance the appreciation of mathematics as a whole. This book is an in-depth account of graph theory, written with such a student in mind; it reflects the current state of the subject and emphasizes connections with other branches of pure mathematics. The volume grew out of the author's earlier book, Graph Theory -- An Introductory Course, but its length is well over twice that of its predecessor, allowing it to reveal many exciting new developments in the subject. Recognizing that graph theory is one of several courses competing for the attention of a student, the book contains extensive descriptive passages designed to convey the flavor of the subject and to arouse interest. In addition to a modern treatment of the classical areas of graph theory such as coloring, matching, extremal theory, and algebraic graph theory, the book presents a detailed account of newer topics, including Szemer\'edi's Regularity Lemma and its use, Shelah's extension of the Hales-Jewett Theorem, the precise nature of the phase transition in a random graph process, the connection between electrical networks and random walks on graphs, and the Tutte polynomial and its cousins in knot theory. In no other branch of mathematics is it as vital to tackle and solve challenging exercises in order to master the subject. To this end, the book contains an unusually large number of well thought-out exercises: over 600 in total. Although some are straightforward, most of them are substantial, and others will stretch even the most able reader.

Editorial Reviews

Review

"...This book is likely to become a classic, and it deserves to be on the shelf of everyone working in graph theory or even remotely related areas, from graduate student to active researcher."--MATHEMATICAL REVIEWS

Product Details

• Hardcover: 394 pages
• Publisher: Springer; 1 edition (July 1, 1998)
• Language: English
• ISBN-10: 0387984917
• ISBN-13: 978-0387984919
• Product Dimensions: 9.8 x 6.5 x 1 inches
• Shipping Weight: 1.6 pounds
• Average Customer Review: 4.8 out of 5 stars  See all reviews (5 customer reviews)
• Amazon Best Sellers Rank: #4,859,949 in Books (See Top 100 in Books)

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Customer Reviews

Most Helpful Customer Reviews

44 of 46 people found the following review helpful:

5.0 out of 5 stars Excellent in content, but somewhat challenging in narrative, January 4, 2003

By 

Todd Ebert (Long Beach California) - See all my reviews

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This review is from: Modern Graph Theory (Paperback)

Bela Bollobas has the rare gift of having both deep mathematical insights, and the ability to eloquently communicate them in a way that is accessible to the average graduate student. In his book "Modern Graph Theory", Bollobas covers just about every exciting area of the subject, and does so in an up-to-date fashion that gives the reader a big picture of each sub-area of the field. The ability to do this not only seems difficult, but also essential, since he himself has written entire books on two of the chapters (extremal graph theory, and random graphs). Just about every major important theorem (including max-flow/min-cut Theorem, and theorems by Menger, Szemeredi, Kuratowski, Erdos/Stone, and Tutte) can be found here, and thus makes this book indispensable for anyone who does research in graph theory, combinatorics, and/or complexity theory. In my opinion the true highlights of this book are indeed those areas he knows best: extremal graph theory, random graphs, and random walks on graphs, the latter of which may be the best introduction to that subject that one will find in a textbook.

My only complaint, at the cost of perhaps half a star, is that his discussions and proofs often seem difficult to follow, as he will state something that to him seems quite obvious, yet to this reader often seemed a bit subtle, and would hence slow down the reading. Indeed, if these off-handed remarks were included as exercises at the end of each chapter, then the number of excercises would have swelled from the current 600 to well over one thousand ! Speaking of which, these 600+ exercises, although also representing another blessing of this book in that they add another degree of depth, tend to lack "starter" exercises, and go straight to the theory. But this is to be expected from a graduate text.

Finally, for the reader whose research significantly intersects with graph theory, but may not be ready or willing to be initiated by Bollabas into the world of graph theory, I would recommend Dietsel's graduate text on the subject. His book covers similar topics, but may be more clearly and transparently, but with less depth and insight.

12 of 14 people found the following review helpful:

5.0 out of 5 stars Good Introduction, too many typos, October 30, 2004

By 

PST "A Reader from Germany" (Eislingen Deutschland) - See all my reviews

This review is from: Modern Graph Theory (Paperback)

I am, what Prof. Bollobas would call a hobby mathematician. Some popular science book arouse my interest in graph theory, and the author of that popular science book recommended this book. I feel it was a vey good introduction to the subject, even though the proofs become challenging at times. His motivation for the subject is always concise but precise, one cannot but notice, that a master of the subject is writing about it.

The only distraction are the enormous number of typographical errors: I counted over 60, and this in a third corrected printing!?!

3 of 4 people found the following review helpful:

4.0 out of 5 stars Bollobas, February 15, 2008

By 

Gokul Swamy "Goks" (USA) - See all my reviews
(REAL NAME)   

This review is from: Modern Graph Theory (Paperback)

This is a very well structured book. However, this book is not amenable to easy reading. The theorem proofs are short and concise with no overt explanations. Bottom line is that reading this book is a an exercise for the brain.

Being an engineer my only grouse about this book is that this book is written for mathematicians and as the author himself claims there are very few practical applications accompanying the theory. But this being a graduate text in mathematics it really cannot be expected to fulfill this need.