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Modern Graph Theory (Graduate Texts in Mathematics) Corrected Edition

4.8 out of 5 stars 5 customer reviews
ISBN-13: 978-0387984889
ISBN-10: 0387984887
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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

About the Author

Bela Bollobas has taught at Cambridge University's Department of Pure Maths and Mathematical Statistics for over 25 years and has been a fellow of Trinity College for 30 years. Since 1996, he has held the unique Chair of Excellence in the Department of Mathematical Sciences at the University of Memphis. Bollobas has previously written over 250 research papers in extremal and probabilistic combinatorics, functional analysis, probability theory, isoperimetric inequalities and polynomials of graphs.

Axler-San Francisco State University
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Product Details

  • Series: Graduate Texts in Mathematics (Book 184)
  • Paperback: 394 pages
  • Publisher: Springer; Corrected edition (October 4, 2002)
  • Language: English
  • ISBN-10: 0387984887
  • ISBN-13: 978-0387984889
  • Product Dimensions: 6.1 x 0.9 x 9.2 inches
  • Shipping Weight: 1.6 pounds (View shipping rates and policies)
  • Average Customer Review: 4.8 out of 5 stars  See all reviews (5 customer reviews)
  • Amazon Best Sellers Rank: #126,026 in Books (See Top 100 in Books)

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Top Customer Reviews

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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.
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2 Comments 52 of 54 people found this helpful. Was this review helpful to you? Yes No Sending feedback...
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Format: 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!?!
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By Gokul Swamy on February 15, 2008
Format: 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.
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Format: Paperback
This book is absolutely precious! It is a little bit weird, but you can get used to it. This book's strongest points are that it is easy to jump around in it, and it contains a wealth of material. It also has incredible numbers of exercises, of greatly varying difficulty levels.

The author's clarity of writing comes out particularly well in the later chapters. In particular, my favourite parts are the discussion of algebraic graph theory, and the discussion of the Tutte polynomial and connections with knot theory. There is also some beautiful use of linear algebra in various parts of the book; some rather strange and difficult results are presented very clearly.

I think this book would be a great purchase for anyone wanting to engage in some self-study in graph theory, or anyone wanting a good reference on graph theory, or anyone wanting to work some hard problems (or easy problems) in graph theory, or someone choosing a textbook for a graph theory course...or...in short, anyone who wants anything to do with graph theory at all.
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Format: Paperback
My profile is the following: I am a phD student in theoretical computer science and I needed a good introduction book to graph theory.
This book is just what I needed...
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