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An in-depth account of graph theory, written for serious students of mathematics and computer science. It reflects the current state of the subject and emphasises connections with other branches of pure mathematics. Recognising 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 flavour of the subject and to arouse interest. In addition to a modern treatment of the classical areas of graph theory, the book presents a detailed account of newer topics, including Szemerdis Regularity Lemma and its use, Shelahs 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. Moreover, the book contains over 600 well thought-out exercises: although some are straightforward, most are substantial, and some will stretch even the most able reader.
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"...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
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最も参考になったカスタマーレビュー
4 人中、4人の方が、｢このレビューが参考になった｣と投票しています。
By polgoe
形式:ペーパーバック
ネットワーク・マッチング・彩色理論・極限的理論・ラムゼー理論といったグラフの中心的な理論のほか、確率論的方法や代数学との関連についても一通り盛り込んであり、演習問題も豊富で入門書としては不足がないと思います。
また、個々の話題の導入や定理の証明などをそれらの背景にある着想まできっちりと分かりやすく記しているため読みやすく、理論的なまとまりとグラフ理論のパズル的面白さを同時に感じることができ、この方面の入門書としてはお薦めの一冊です。
また、個々の話題の導入や定理の証明などをそれらの背景にある着想まできっちりと分かりやすく記しているため読みやすく、理論的なまとまりとグラフ理論のパズル的面白さを同時に感じることができ、この方面の入門書としてはお薦めの一冊です。
Amazon.com で最も参考になったカスタマーレビュー (beta)
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5つ星のうち 4.8
5件のカスタマーレビュー
49 人中、47人の方が、｢このレビューが参考になった｣と投票しています。
5つ星のうち 5.0
Excellent in content, but somewhat challenging in narrative
2003/1/5
By Todd Ebert
- (Amazon.com)
形式:ペーパーバック|Amazon.co.jpで購入済み
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.
18 人中、16人の方が、｢このレビューが参考になった｣と投票しています。
5つ星のうち 5.0
Good Introduction, too many typos
2004/10/31
By PST
- (Amazon.com)
形式:ペーパーバック
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!?!
The only distraction are the enormous number of typographical errors: I counted over 60, and this in a third corrected printing!?!
7 人中、6人の方が、｢このレビューが参考になった｣と投票しています。
5つ星のうち 4.0
Bollobas
2008/2/16
By Gokul Swamy
- (Amazon.com)
形式:ペーパーバック
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.
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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5つ星のうち 4.8
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