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Title: Modern Graph Theory by Bela Bollobas, Sheldon Axler, F. W. Gehring ISBN: 0-387-98488-7 Publisher: Springer Verlag Pub. Date: 01 July, 1998 Format: Paperback Volumes: 1 List Price(USD): $47.95 |
Average Customer Rating: 5 (2 reviews)
Rating: 5
Summary: Excellent in content, but somewhat challenging in narrative
Comment: 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.
Rating: 5
Summary: A good introduction book
Comment: 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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Title: Graph Theory (Graduate Texts in Mathematics, 173) by Reinhard Diestel ISBN: 0387989765 Publisher: Springer Verlag Pub. Date: 15 January, 2000 List Price(USD): $49.95 |
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Title: Random Graphs by Béla Bollobas, W. Fulton, A. Katok, F. Kirwan, P. Sarnak ISBN: 0521797225 Publisher: Cambridge University Press Pub. Date: 15 January, 2001 List Price(USD): $47.00 |
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Title: The Probabilistic Method by Noga Alon, Joel H. Spencer ISBN: 0471370460 Publisher: John Wiley & Sons Pub. Date: 11 August, 2000 List Price(USD): $99.95 |
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Title: Approximation Algorithms by Vijay V. Vazirani ISBN: 3540653678 Publisher: Springer Verlag Pub. Date: 09 August, 2001 List Price(USD): $39.95 |
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Title: Combinatorial Optimization : Algorithms and Complexity by Christos H. Papadimitriou, Kenneth Steiglitz ISBN: 0486402584 Publisher: Dover Pubns Pub. Date: 07 July, 1998 List Price(USD): $18.95 |
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