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Modern Graph Theory (Graduate Texts in Mathematics) (Englisch) Taschenbuch – 4. Oktober 2013

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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


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.

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The basic concepts of graph theory are extraordinarily simple and can be used to express problems from many different subjects. Lesen Sie die erste Seite
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Amazon.com: HASH(0x9c98d7ec) von 5 Sternen 5 Rezensionen
52 von 54 Kunden fanden die folgende Rezension hilfreich
HASH(0x9cd7e2b8) von 5 Sternen Excellent in content, but somewhat challenging in narrative 5. Januar 2003
Von Todd Ebert - Veröffentlicht auf Amazon.com
Format: Taschenbuch Verifizierter Kauf
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.
20 von 22 Kunden fanden die folgende Rezension hilfreich
HASH(0x9ce2d72c) von 5 Sternen Good Introduction, too many typos 30. Oktober 2004
Von PST - Veröffentlicht auf Amazon.com
Format: Taschenbuch
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!?!
11 von 12 Kunden fanden die folgende Rezension hilfreich
HASH(0x9da01ccc) von 5 Sternen Bollobas 15. Februar 2008
Von Gokul Swamy - Veröffentlicht auf Amazon.com
Format: Taschenbuch
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.
9 von 11 Kunden fanden die folgende Rezension hilfreich
HASH(0x9ce2890c) von 5 Sternen I have so many good things to say about this book... 11. Juni 2006
Von Alexander C. Zorach - Veröffentlicht auf Amazon.com
Format: Taschenbuch
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.
11 von 47 Kunden fanden die folgende Rezension hilfreich
HASH(0x9d36a06c) von 5 Sternen A good introduction book 18. Januar 2001
Von olivier powell - Veröffentlicht auf Amazon.com
Format: Taschenbuch
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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