Book Description

Customer Reviews (7)

The Holy Grail of Graph Theory
This is, for all purposes, the Holy Grail of Graph Theory.It is older, but still very much applicable.As a computer scientist (instructor and Masters degree student), I highly recommend this for students studying Discrete Mathematics and Graph Theory.

It has several examples throughout and the presentation is excellent.Many books on mathematics from this 'era' tend to be overly wordy and full of poorly explained examples and topics.This book suffers very little from this problem.

I recommend this to anyone looking for a good introductory book on Graph Theory.It also makes an excellent reference book for even the experienced individual.

Chemistry, Neural Nets, Matrix Manipulation -- all here
While working on my math degree I wanted some light reading on Graph Theory for completing some side projects.This book hit the spot, and the examples saved me.

Chartrand uses applications from every field of interest (e.g. finance, Chemistry, Physics, games, social psychology, computers, etc.)Who would have thought that while reading a math book that a friendly discussion of social psychology would pop-up?Well, that's how Chartrand is able to keep us moving through the pages; he uses the common to reveal the mysteries of Graph Theory. Who doesn't know about the Tower of Hanoi or the Knight's Tour or the one-boat-fox-and-chickens problems? All of these classics make for ready connecting points, leading us into profound restatements of well-known problems.Not much space is devoted to creating artificial problems for which we must be convinced need solving, and so the book is rather thin (a real bonus for those of us who don't want to spend a month in a math book).

Picking up the book after having read it so long ago, I was happy to find that the chapters are nearly autonomous and can be profitably read by themselves -- so keep it as a reference and jump in as the need arises, you'll be both entertained and mathematically illumined.

My only complaint is that the writing style is rather thick with mathematical lingo (seemingly) for the sake of being technically pithy.I am not convinced that such is necessary for a good math book.

Excellent overview for those with solid math background
This book is excellent, especially if you already have a pretty good background in math.I don't... high school math through calculus, almost all of which I've forgotten.But the appendix gets you up to speed on the basics of sets, functions, and proofs using mathematical induction.That was enough for me to get a lot out of all but the last chapter, which deals with matrices and groups.Although I have to admit that I occasionally needed to read an example four or five times before I really got it.

I definitely recommend this book for anyone interested in graph theory and to any serious software developer (which I why I picked it up).The ideas presented are directly applicable to that line of work.

Fantastic Book!
Most books assume that the reader has a month to carefully read the book.In reality, the reader often has a day or two and needs a solid understanding of the material but not a really detailed understanding.This book is great because it quickly and clearly covers all of the necessary concepts.What else can you ask for?

Great introductory book to graph theory
This book is really god and informative, the topics are clearly explained even to the most novice of readers. Many practice problems.Highly recommended for computer science major. ... Read more

Book Description

Far more "user friendly" than the vast majority of similar books, this volume is truly written with the unsophisticated reader in mind.The pace is leisurely, but the authors are rigorous and maintain a serious attitude towards theorem proving throughout. Emphasizes "Active Reading" throughout, a skill vital to success in learning how to write proofs. Offers two sections on probability (2.4 and 2.5). Moves material on depth-first search, which previously comprised an entire (very short) chapter, to an earlier chapter where it fits more naturally. Rewrites section on RNA chains to include a new (and easier) algorithm for the recovery of an RNA chain from its complete enzyme digest. Provides true/false questions (with all answers in the back of the book) in every section. Features an appendix on matrices. A useful reference for mathematics enthusiasts who want to learn how to write proofs.

Customer Reviews (9)

Incomprehensible, Poorly Explained Material
This was required for a math class I was taking.In general the concepts lacked extensive explanations, feeling more like an overview of major topics.If you do not have an outside sourceof information such as a TA, professor, or another reference book it will be very difficult for you to learn the subject matter from this book.

Bareable Book
This book is okay. Not the best but not that bad. If you have choice look for something better. If your stuck with this one then its not too bad.

Too discrete!!!
It is one thing to learn math.It is another thing to read it from a textbook.Although discrete mathematics is not meant to be all that numerically focused, I do not recommend using this text at all.There are very few examples to accompany the new content and the explanations are not clear.Also, the section review problems are NOTHING like the material presented.Yes, it is imperative to think like a mathematician, but the problems are worded much too differently than what is taught.Do not expect to do well in a course using this text unless you have a helpful instructor!

An excellent choice for discrete if your emphasis is graphs
As a teacher of discrete mathematics, I must constantly scan new books in the never-ending search for the best one with appropriate content and level. The course that I teach is required and early in the computer science major. It also provides the mathematical foundation for all of the later computer science courses.Therefore, any book that I use must demonstrate mathematical proofs, but not at too high a level. Coverage of fundamental topics such as propositional logic, sets, relations and functions; basic combinatorics and induction are a requirement.
This book covers these fundamentals at exactly the level of rigor that I need. There are some proofs, but nothing that is beyond the motivated freshman/sophomore who is receiving the appropriate direction. However, I will not be adopting it because of the large amount of graph theory, which is approximately forty percent of the book. In our class we do cover some graph theory, but prefer to spend less time on it than this book would allow. Our department recently added a course in graph theory, so we only need to touch on the basics of graphs in discrete mathematics.
Therefore, while the book is not suitable for my needs, it would be a perfect fit for anyone teaching discrete mathematics where there was an emphasis on graph theory. In fact, the second half of the book could serve as a starter text for our course in graph theory.

it is satisfactory
This text was designed mainly for young university students with the goal of introducing concepts such as induction to as well as, of course, some introductory descrete math and graph theory, with the former (induction, etc.) being as important as the latter. This is not a comprehensive text and was not intended to be so. It is a pleasent bridge to more mathematically correct way of thinking. Proofs are emphasized, not numerical answers (in most sections). Famous proofs are displayed and are incorperated in a non-trivial way. This book is applicable for mathematics and computer science students alike and the questions have a good spread of difficulty. I recommend this book to anyone interested in something more than high school math. ... Read more

Book Description
This book fills a need for a thorough introduction to graph theory that features both the understanding and writing of proofs about graphs. Verification that algorithms work is emphasized more than their complexity.An effective use of examples, and huge number of interesting exercises, demonstrate the topics oftrees and distance, matchings and factors, connectivity and paths, graph coloring, edges and cycles, and planar graphs.For those who need to learn to make coherent arguments in the fields of mathematics and computer science. ... Read more

Customer Reviews (14)

Not bad
We used this for a Computer Science class on Graph Theory, and I remember more than one student complaining about the book. Generally speaking, what people found most disconcerting about the text was its level of abstraction, and "lack of motivation" for the theorems provided. In my experience, these complaints are frequently leveled by non-mathematicians at books that are clearly NOT non-mathematical; West's book falls into this category. This is, first and foremost, a book for mathematicians.

As pointed out by other reviewers, the book isn't perfect. There are a lot of errors, although you can obviously deal with these if you read the errata. West also has the habit of sometimes presenting a theorem completely out of the blue, which can cause some confusion. That said, the book does a very good job overall. Graph theory is an exceptionally beautiful subject, but it's easy to obscure that in a theorem/proof/theorem didactic haze. West has an agenda, and therefore the book has a discernible structure, which brings out the beauty of the area. The chapters on coloring and planar graphs are particularly strong, although the most interesting chapter for me was the one on additional topics; the sections on matroids, Ramsey theory, random graphs and spectral graph theory, while far from comprehensive, provide good introductions. Another strong aspect of the book are the exercises; these range from very easy to very difficult, the latter being from major papers in graph theory. The hints section at the end of the book is quite helpful here.

Overall, a very good book. I didn't know anything about graph theory before I started reading it, but I had a professor to help me through the rough spots, so perhaps it's not exactly ideal for self-study. If you've been exposed to the basics before though, it's definitely worth taking a look at.

Good middling book
The treatment is logically rigorous and impeccably arranged, yet, ironically, this book suffers from its best feature: it is comprehensive. As a book becomes more encyclopedic, it becomes less useful for pedagogy. Introduction to Graph Theory is somewhere in the middle. It is an adequate reference work and an adequate textbook. Steering a middle course, the book is bound to dissatisfy people with specific needs, but readers needing both a reference and a text will find the book satisfying.

If you buy it for pedagogical purposes, be prepared to consult other works for a more intuitive approach. Introduction to Graph Theory presents few models, relying instead on logically rigorous development. Personally, I'm for both, but that takes up space, meaning less material can be covered.

I'm glad I bought the book, and I will keep it for a future reference.

Graph lovers' book
West is enthusiastic about graph theory.I do not recommend this book for independent study, nor would I recommend it for a first-time student of graph theory.It is called "Introduction to Graph Theory", not because it is an appropriate introductory text for new students, but because it covers a broad area of the subject.I recommend it for a student who has read at least one lower-level introductory text and would like to round out their knowledge of graph theory in a more in-depth way.
I have two problems with this book.They both stem from the fact that it reads more like a collection of journal articles than like a cohesive text book.One is that his notation is very specific--he does not always use the most common form of notation, and this means that dipping into the book is difficult.The second problem for me is that West defines many things that I do not feel need defining.Rather than using a short description of a certain type of graph whenever he refers to it, he will give it a label.Again, this makes dipping into his text rather difficult, especially since many of the things he defines are not generally given a definition.Both of these would be perfectly reasonable for a journal article, but seem rather out of place in a large textbook--his definitions particularly clutter up his work.Perhaps West is more used to writing papers than textbooks.
Having said that, West is very knowledgeable and enthusiastic.His exercises are wonderful, marked with a (-) for easy, a (+) for difficult, a (!) for particularly instructive, and a (*) for problems based on optional material.Several of the (!) problems I have worked required me to actually look up the paper that they are based on for the final solution--which is possible due to his excellent citations.His index of works cited is an education in itself, and any student wishing to pursue a specific area in greater depth will find his book an wonderful gateway.

My perspective: I am an undergraduate student doing summer research in graph theory, working under a professor.

Just a pile of theorems without much insight
This book is an average book on graph theory. Although the author is an authority in the field, he seems to just have collected a bunch of theorems and put them together "a la" copy-and-paste, without filling up the gaps with useful insights.Intuition is always the key on a book that claims to be introductory, and this book lacks a lot of that. Probably useful as a reference book, but again not as "Introduction to Graph Theory" (and to be used as a "handbook of graph theory" it would need much more material.

Pretty good
Level of the book: 3rd-4th year undergrad or 1st-2nd year grad (pretty big range).

Don't let other reviews fool you.This book does an excellent job covering the material at hand, especially given the task West set out to achieve.The book basically stands alone thanks to thorough appendices and a fair amount of examples, plus lots of problems (mostly proofs).Because this material is proof-based, I cannot suggest that this book could stand alone, but that someone else should review problems and such.

When I first was reading this book, I ignored the appendices, and that was my downfall.Once I started using all the tools in this book, things started coming together.Because of the intricate design, I would recommend this book only to people who are serious about a thorough introduction to graph theory.That is, actually proving many of the theorems that play a central role in this introduction.For a simple introduction to concepts, I would recommend Trudeau's book, "Introduction to Graph Theory," which is a good read and introduces a few of the ideas and definitions of graph theory, but does not focus on proofs.

My only major quarrel with this book is that it is completely void of color!This would be EXTREMELY useful in this book because many of the diagrams are complicated and different color labels would make things much clearer (instead of bolding lines and such).The increased price of the book would certainly be worth the clarity from color.There are also some typos throughout the book, but none too major (that have been noticed).

Overall, I would highly recommend this book over any other, but consider waiting until an edition with color comes out. ... Read more

Book Description
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. ... Read more

Customer Reviews (5)

Bollobas
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.

I have so many good things to say about this book...
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.

Good Introduction, too many typos
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!?!

Excellent in content, but somewhat challenging in narrative
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 froma 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.

A good introduction book
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... ... Read more

Book Description

Customer Reviews (5)

Fun intro to graph theory
I like this book as an intro to graph theory.I already had a little background in graph theory and a graduate degree in mathematics before I got this book, but I think that less experienced readers with an interest in pure math will enjoy this book.It's readable and conversational, and special attention is given to introducing pure mathematics and proof.

Nice Introduction
One of the better Dover books I've picked up... but keep in mind it is a (very basic) introduction.

The book gives an introduction to graph theory (take the "introduction to" part of the title very seriously).To give an idea of the depth of this book, I read this book in about 6 hours prior to taking a course in graph theory (an undergraduate and graduate student mixed course), and the material in the book was covered in class in about 4 lectures (there were about 30 lectures in the course).This isn't to say the book isn't good (because it is), but I just have to emphasize it is a basic introduction.

What gives this book 5 stars is that it was written very well and made the material very interesting.I would recommend this book to someone looking to understand the very basics of graph theory, but I would not to someone looking for a thorough introduction to graph theory.

For reference, titles of chapters: 1) Pure Mathematics; 2) Graphs; 3) Planar Graphs; 4) Euler's Formula; 5) Platonic Graphs; 6) Coloring; 7) The Genus of a Graph; 8) Euler Walks and Hamilton Walks.

Concise and very well explained
Chapter on planar graphs is superbly done, with very easy to understand proofs and plenty of illustrations. Overall, a great introductory text

Graph theory in (good) words.
This book make you want to know more about graph theory. The concepts are first intuitively explained and then formally stated. The numerous examples are completely treated and then easy to follow. R. Trudeau devoted a largepart of the book to the puzzling problems of planar graphs and coloring andexplains them in a very pleasant manner. As a result, these problems almostappear as trivial (which of course is not the case).

The main criticism Iwould make is the following. This book is a corrected and enlarged versionof another book. Unfortunately, the updating is not very convincing whenthe "four color problem" is a conjecture in the body of the bookand a theorem in footnotes and afterwords.

A fascinating start into graph theory.
Mr. Trudeau has done a fabulous job of introducing graph theory in a way which is understandable and intellectually provocative. He mentions that some of the problems are easy, and that some have been unsolved. In bothcases, they both are fully illustrative of the subject matter. If you wantto begin exploring graph theory, this book is for you! ... Read more

Book Description
Student's love Schaum's--and this new guide will show you why! Graph Theory takes you straight to the heart of graphs. As you study along at your own pace, this study guide shows you step by step how to solve the kind of problems you're going to find on your exams. It gives you hundreds of completely worked problems with full solutions. Hundreds of additional problems let you test your skills, then check the ansers. So if you want to get a firm handle on graph theory--whether to ace your graph course, to supplement a course that uses graphs, or to build a solid basis for future study--there's no better tool than Schaum's. This guide makes a wonderful supplement to your class text, but it is so comprehensive that it can even be used alone as a complete graph theory independent study course! ... Read more

Customer Reviews (4)

Not up to the standard of most Schaum's outlines
I have bought and used many Schaum's outlines on various subjects in math and science, and I would say that this outline on graph theory is one of the worst. Most Schaum's outlines give you the theory in small doses, with plenty of diagrams to explain the concepts. This outline reads more like one of the textbooks on the subject, however. Theorems and their illustrations are poorly presented, and the author could not have made the subject matter drier and more unappealing if he had tried. You might be able to get something out of it if you are a student of pure mathematics, but you will definitely be disappointed in this book if you are a computer science student. If you are already using a bad textbook for a class in graph theory, this book will only add to your collection of bad unreadable texts on the subject. For computer science students, I suggest that you check out the chapters on graph algorithms in Introduction to Algorithms by Cormen et al. That book has pseudocode, explanations, and diagrams to help you work out implementations of various graphing algorithms.

This book is $$$ for a reason
This book was an absolute hell to contend with.I've taken two courses in Graph Theory, using Robin J. Wilson's Introduction to Graph Theory and this cheap broadsheet, respectively.Wilson's book is the one to use!It's extremely well-written, even fun to read--the reviews on Amazon will bear that out.

In the second graph theory course that I took (to refresh and refine my understanding), the professor chose the Schaum text solely for its low cost--he thought he was doing the students a service.Hardly.

No thought whatsoever has been put into the readability of this book.The tiny dark-grey font on light-grey paper is a simple enough design flub that makes reading past even two or three pages at a time almost unbearable.Defining terms is seen as a chore to be compacted--a single page at the beginning of each chapter might try to define 10-15 terms, just to get them out of the way.It becomes a mess of bold print that the reader is forced to continually return to because the definitions come with no context nor examples by which to remember them.In the end, the reader realizes that 2/3 of the book is just list after list of badly-worded questions following under-scripted lessons.

Look, it's not even worth writing any more about, the text frustrates me so much.There's only two other reviews on this page, and I'd place money on them being written by the author himself.Save yourself the $$$ and the hassle, and just go buy Wilson's book.Trust me.

Good Book. I recommend it.
In general, the book not requires study in advance, but it is better for reference. I'm a software engineer and the book's treatment of "Shortest Path" and "Connectivity" problems is very usefull. Good for fast remember of the subject.

A smooth surfinginto the amazing world of graph theory
In this book one can find a practical survey of both principles and practice of graph theory, with great coverage of the subject. The outhor provides a lots of solved problems, with losts of theory proofs and allwith great clarity and common reasoning. The outhor gets you enter thesubject step by step from the easy problems to the hardest with greatskill. Also the algorithms on graphs presented in this book, and in generalthe algorithmic approach of this book are presented most clearly. Youwouldn't leave this book until you'l finish read it and understand graphtheory. Finally you would fill that at least on one branch of mathematicsyou are well sitted. ... Read more

Book Description

Once considered an “unimportant” branch of topology, graph theory has come into its own through many important contributions to a wide range of fields – and is now one of the fastest-growing areas in discrete mathematics and computer science. This practical, intuitive book introduces basic concepts, definitions, theorems, and examples from graph theory. Presents a collection of interesting results from mathematics that involve key concepts and proof techniques. Covers design and analysis of computer algorithms for solving problems in graph theory. Discusses applications of graph theory to the sciences. Includes a collection of graph algorithms, written in Java, that are ready for compiling and running. For anyone interested in learning graph theory, discrete structures, or algorithmic design for graph problems.

Customer Reviews (1)

Good Introduction
This is a very good introductory book on Graph Theory. If you don't want to be overwhelmed by Doug West's, etc., and yet receive a decent introduction to the topic, this book is your best bet. It covers all the topics required for an advanced undergrad course or a graduate level graph theory course for Math, engineering, operations research or computer science students in good depth and details. There are good examples and interesting exercises; some computer codes (JAVA) are also available in the book implementing some of the algorithms.
I would say O.R. and CS people will benefit a lot from it both as a reference or a textbook if adapted for a one semester graduate course. The only drawback is the price!
... Read more

Book Description
Already aninternational bestseller,with the release of this greatly enhanced second edition, Graph Theory and Its Applications is now an even better choice as a textbook for a variety ofcourses -- a textbook that will continue to serve your students as a reference for years to come.The superior explanations, broad coverage, and abundance of illustrations and exercises that positioned this as the premier graph theory text remain, but are now augmented by a broad range of improvements. Nearly 200 pages have been added for this edition, including nine new sections and hundreds of new exercises, mostly non-routine.What else is new?· New chapters on measurement and analyticgraph theory · Supplementary exercises in each chapter - ideal for reinforcing, reviewing, and testing. · Solutions and hints, often illustrated with figures, to selected exercises - nearly 50 pages worth · Reorganization and extensive revisions in more than half of the existing chapters for smoother flow of the exposition · Foreshadowing - the first three chapters now preview a number of concepts, mostly via the exercises, to pique the interest of readerGross and Yellen take a comprehensive approach to graph theory that integrates careful exposition of classical developments with emerging methods, models, and practical needs. Their unparalleled treatment provides a text ideal for a two-semester course and a variety of one-semester classes, from an introductory one-semester course to courses slanted toward classical graph theory, operations research, data structures and algorithms, or algebra and topology. ... Read more

Customer Reviews (6)

Horrible textbook
Reads like a dictionary, each page is nothing more than bullet points that alternate between definitions and corollaries.Proofs are typically very short: explained and illustrated in no more than a quarter of a page.More appropriate as a reference manual than a textbook for a class.

Plain and simple: EXCELLENT book

This is a superb book for an introduction to graph theory. It is not just a pile of theorems as other books you'll find in this field. It presents insight and intuition first, and then it gives the necessary formal treatment. The topics covered are perfect, in the right order.Extremelly recommended for anyone eagerly wanting a first contact with this exciting field, as well as for any graph theory instructor looking for the right book to follow in class.

great, comprehensive introduction
Regardless of whether you just want to implement a couple of graph algorithms or get into the guts of graph theoretic proofs, this book should come in as a great resource.

In over 500 pages, this book covers a lot of ground beyond the basics, such as topology of graphs, graph operations and mappings, voltage graphs, and surface imbeddings.Definitions are very clear, propositions and proofs are stated very clearly, and there are shrink-wrapped algorithms if you just want to apply them.

Requiring no previous knowledge of abstract algebra or graph theory, this is a great resource to have in your bookshelf.

not recommended
This book was used for my undergraduate course in introductory graph theory, which was split between math and computer science students. I found that this book left to be desired. The definitions are imprecise and often inconsistent with those that are standard, and much of the notation used is not standard. I would not recommend this book as a reference or for advanced students.

A great link between math and computer sciences
Professors Gross and Yallen have written a great book on "practical" graph theory that can be used in math or computer sciences courses alike. The book is very well organized and its chapterscan be read on almost any sequence, allowing instructors to skip sectionsor give special emphasis to certain more interesting subjects.

The textcan be used in a one semester introductory graduate course in graph theoryin a CS or math department, an advanced undergraduate seminar or as areference book for an undergraduate course in discrete math.

Of specialinterest are the sections on Huffman trees and voltage graphs. The sectionon Hoffman trees is especially interesting tocomputer scientists. Ibelieve this is the first book that devotes an entire section to thetheoretical treatment of this very useful subject. Prof. Gross is a pioneerin voltage graphs and the treatment of this somewhat esoteric subject islucid and complete.

Overall this textbook is excellent. The writing isclear and precise and the knowledge needed to read it is that of anadvanced undergraduate student. However, the book could benefit fromsolutions to the exercises, or at least some selected exercises, somecomputer sciences oriented "practical" examples and projects andan instructor's manual. ... Read more

Book Description

Customer Reviews (1)

A book on graph theory
Pearls in graph theory begins informally and at an elementary level, suitable for a substantial freshman-sophomore course. After intuitive introductions, concepts and theory are developed with increasing depth, leading into material for a good intermediate-level course. Included also are appropiate open conjetures on, for example the Oberwohlfach problem, magic and antimagic graphs, and colorings of "earth-moon" maps. In addition, for me the final three chapters are asplendid, enticingly elementary yet comprehensive introduction to topological graph theory. Essentially no othr introductory text presents thedepth, breadth, and fun of topological graph theory as does this book. ... Read more

Book Description

The third edition of this standard textbook of modern graph theory has been carefully revised, updated, and substantially extended. Covering all its major recent developments it can be used both as a reliable textbook for an introductory course and as a graduate text: on each topic it covers all the basic material in full detail, and adds one or two deeper results (again with detailed proofs) to illustrate the more advanced methods of that field.

Customer Reviews (1)

Somewhat technical but well written
Not a book that you can really judge well on one reading:
study is necessary.
The authorpresents the diagrams and proofs well.
He covers the main topics in graph theory:
"Matching,"
"Connectivity,"
"Planar Graphs,"
"Coloring,"
"Flows
"Ramsey Theory for Graphs,"
"Hamilton Cycles,"
"Random Graphs,"
"Minors, Trees and Well-Quasi-Ordering."
and Infinite graphs.
It is a text for graduate school topology in which the theory of graphs
is covered in detail.
I could wish for more on Ramsey theory,
but the author's are the only graph diagrams in that area that I've found. ... Read more

Book Description
Beautifully written and elegantly presented, this book is based on 10 lectures given at the CBMS workshop on spectral graph theory in June 1994 at Fresno State University. Chung's well-written exposition can be likened to a conversation with a good teacher--one who not only gives you the facts, but tells you what is really going on, why it is worth doing, and how it is related to familiar ideas in other areas. The monograph is accessible to the nonexpert who is interested in reading about this evolving area of mathematics. ... Read more

Customer Reviews (1)

Elegant and coherent, but a bit dry and unmotivated
This book is elegant and accessible, with a coherent presentation, but is a bit dry and unmotivated. The book would benefit from more applications, which should not be hard to find. I felt like Chapter 8 was the high point of the book, with a discussion of random walks, a matrix-tree theorem and invariant field theory.

The researcher who needs an arsenal of technical results in a clear style will find it here; the student who desires some added perspective may come away somewhat dissatisfied. ... Read more

Customer Reviews (4)

Charming introduction
This author has a charming writing style, although he suffers from a mathematician's sense of humor.A light introduction to graph theory, suitable for a beginning undergraduate student.Nothing is covered particularly in-depth, and the more difficult proofs are passed over and left to the reader to find and master.The exercises are very important--many of the most important theorems are hidden in there.This text is suitable for independent study, although an advisor would be helpful simply because the theorems hidden in the exercises make you want to have your homework checked.
A further note on proofs: many of those that the author does include are constructionist, and seem to involve a lot of hand-waving.There are very few rigorous proofs, and a teacher using this book should instruct his or her students in the more formal approach to graph theory proofs.This text could benefit from including more.

On the whole: nice diagrams, good notation, good order of material, and very accessible.

I read this text during an undergraduate combinatorics course after having taken a semester of introductory graph theory.

Not at this price
This is a very, very thin introductory work on graph theory.

It loses one star because the section numbering and the chapter numbering aren't aligned correctly. (The section numbers increase monotonically from 1 to N. Chapter breaks are inserted almost randomly as a way of grouping sections.)

It loses another star because it doesn't serve the needs of beginners very well. As a previous reviewer has pointed out, it doesn't contain many examples, and results are often stated with only sketch proofs.

It loses one final star because of its ridiculous price. For the same dollar amount, one could buy a good introductory book (such as Chartrand's "Introduction to Graph Theory"), a Schaum's outline (for solved problems), and a decent high-level book for mathematical depth.

On the positive side, Prentice did print this thing on good paper...

The worst book in graph theory
I have found this book difficult to read because of its lack of examples and theorems.Many famous examples and theorems are left as exercises.Many of them are too difficult for a beginner.The book just state some basic defintion and theorem without examples, and even some proofs of the theorems are not complete.Many algorithms are skipped or illustrated badly.I can give no reason for the beginner to buy this book. I would suggest the reader to see "A first Look At Graph Theory" by John O. Clark

Great introductory text!!
A great -and gentle - introduction to Graph Theory...clear definitions and examples, great figures,useful exercises, and even some cleverquotes.Everything you could ask for - if only all texts were this clearand well-organized.This was my first foray into the topic, and Wilson'stext made it enjoyable. ... Read more

Book Description
This is a textbook on graph theory, especially suitable for computer scientists but also suitable for mathematicians with an interest in computational complexity. Although it introduces most of the classical concepts of pure and applied graph theory (spanning trees, connectivity, genus, colourability, flows in networks, matchings and traversals) and covers many of the major classical theorems, the emphasis is on algorithms and their complexity: which graph problems have known efficient solutions and which are intractable. For the intractable problems a number of efficient approximation algorithms are included with known performance bounds. Informal use is made of a PASCAL-like programming language to describe the algorithms.

A number of exercises and outlines of solutions are included to extend and motivate the material of the text.Download Description
This is a textbook on graph theory, especially suitable for computer scientists but also suitable for mathematicians with an interest in computational complexity. Although it introduces most of the classical concepts of pure and applied graph theory (spanning trees, connectivity, genus, colourability, flows in networks, matchings and traversals) and covers many of the major classical theorems, the emphasis is on algorithms and thier complexity: which graph problems have known efficient solutions and which are intractable. For the intractable problems a number of efficient approximation algorithms are included with known performance bounds. Informal use is made of a PASCAL-like programming language to describe the algorithms. A number of exercises and outlines of solutions are included to extend and motivate the material of the text. ... Read more

Book Description
This book evolved from several courses in combinatorics and graph theory given at Appalachian State University and UCLA. Chapter 1 focuses on finite graph theory, including trees, planarity, coloring, matchings, and Ramsey theory. Chapter 2 studies combinatorics, including the principle of inclusion and exclusion, generating functions, recurrence relations, Pólya theory, the stable marriage problem, and several important classes of numbers. Chapter 3 presents infinite pigeonhole principles, König's lemma, and Ramsey's theorem, and discusses their connections to axiomatic set theory. The text is written in an enthusiastic and lively style. It includes results and problems that cross subdisciplines, emphasizing relationships between different areas of mathematics. In addition, recent results appear in the text, illustrating the fact that mathematics is a living discipline. The text is primarily directed toward upper-division undergraduate students, but lower-division undergraduates with a penchant for proof and graduate students seeking an introduction to these subjects will also find much of interest.
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Customer Reviews (4)

Glorious
The authors of this book have managed to teach, in a complete and thorough manner, enough material to fill a book more than twice the size of this one.Do not mistake its brevity for a Rudin-esque lack of explanation, or for a lack of substance.Explanations are provided, a good deal of material is covered, and the book remains so concise and to the point that I have no complaints whatsoever.

Very few math books lend themselves well to being read cover-to-cover, but the unassuming nature of this book makes it perfect for a leisurely and fun read, or for a classroom.

Fans of the writing style of Joseph Gallian's "Contemporary Abstract Algebra" will enjoy this book's ability to present material in a friendly way without oversimplifying.

Buy this book.

A truly elegant introduction to combinatorics
Unlike its competitors, this book states simple concepts simply.It gives an excellent selection of the most important techniques and examples, without endlessly repeated "real-world" applications.In 80 pages, it covers the most interesting topics in graph theory, including:Cayley's tree-counting theorem, vertex coloring (with proof of the 5-Color Theorem), Hall matching theorem, Ramsey numbers, and stable marriage. Another 80 pages contains the main concepts of enumeration: elementary combinations (poker hands), inclusion-exclusion, generating functions for Fibonacci and Catalan numbers, Polya counting of symmetry classes, Stirling numbers.There is final section on infinite sets and graphs.

The book covers quite as much as similar ones of twice the length.Finally, a textbook which is not afraid to be brief!

Perfect book for self teaching
I am a math student with Indiana University working out of this book for independent study credit.When my adviser and I sat down to discuss books, we sifted through 10 to 12 books, and it was clear from the start that this book was the best.And I haven't changed my mind since.The book is clear, concise, and easy to read.Excellent for anyone who is teaching themselves, which of course means it's great for a full course with actual instructors.

What an introductory book on combinatorics should be
Little did I expect of a book that has seemingly not garnered that much attention among professors and students (at least the lack of reviews in Amazon.com might serve as a confirming instance of that speculation), but come exam time, the book proved that such prejudice is outright foolish.

The authors must really love both the field and writing about it, for their overflowing exuberance readily transfers to the pages. Pictures and humor are never a scarcity here: the authors took no shame providing both; a curious but pleasurably fresh anomaly in the often dry and coldly serious world that is mathematics writing. ... Read more

Book Description
The Handbook of Graph Theory is the most comprehensive single-source guide to graph theory ever published. Best-selling authors Jonathan Gross and Jay Yellen assembled an outstanding team of experts to contribute overviews of more than 50 of the most significant topics in graph theory-including those related to algorithmic and optimization approaches as well as "pure" graph theory. They then carefully edited the compilation to produce a unified, authoritative work ideal for ready reference.Designed and edited with non-experts in mind, the Handbook of Graph Theory makes information easy to find and easy to understand. The treatment of each topic includes lists of essential definitions and facts accompanied by examples, tables, remarks, and in some areas, conjectures and open problems. Each section contains a glossary of terms relevant to that topic and an extensive bibliography of references that collectively form an extensive guide to the primary research literature.The applications of graph theory are fast becoming ubiquitous. Whether your primary area of interest lies in mathematics, computer science, engineering, or operations research, this handbook holds the key to unlocking graph theory's intricacies, applications, and potential. ... Read more

Customer Reviews (2)

Comprehensive supplementary reference
Don't try to learn anything for the first time from this. In each of the book's 54 sections, information is delivered as bulleted lists of definitions and theorems (called "facts") and there are extensive references to the literature. To maximize brevity, there is seldom any narrative introduction and only a few brief examples. No proofs, just references to them.

I noted two significant gaps in coverage. Since the main application of graph theory is in computer science, much of the Handbook relates to that field, yet there is no chapter on computational complexity. The other absent topic is scale-free graphs.

Nothing more than a handbook
As the title indicates, this is not a textbook, but a handbook. Theinterest of this one is to have pointers to the literature and to cover as much as possible of graph theory, so don't expect to find much details about something particular. I don't think it's useful for anything else than having a "close to hand" access to most of graph theory, hence only three stars for this limited interest compared to the relatively high price. ... Read more

Book Description

Graph theory is a flourishing discipline containing a body of beautiful and powerful theorems of wide applicability. Its explosive growth in recent years is mainly due to its role as an essential structure underpinning modern applied mathematicscomputer science, combinatorial optimization, and operations research in particularbut also to its increasing application in the more applied sciences. The versatility of graphs makes them indispensable tools in the design and analysis of communication networks, for instance.

Customer Reviews (1)

excellent
i found that this book is excellent , espicially for those who want in the future to go deeply in their research
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Book Description
Algorithmic Graph Theory and Perfect Graphs, first published in 1980, has become the classic introduction to the field. This new Annals edition continues to convey the message that intersection graph models are a necessary and important tool for solving real-world problems. It remains a stepping stone from which the reader may embark on one of many fascinating research trails.

The past twenty years have been an amazingly fruitful period of research in algorithmic graph theory and structured families of graphs. Especially important have been the theory and applications of new intersection graph models such as generalizations of permutation graphs and interval graphs. These have lead to new families of perfect graphs and many algorithmic results. These are surveyed in the new Epilogue chapter in this second edition.

· New edition of the "Classic" book on the topic
· Wonderful introduction to a rich research area
· Leading author in the field of algorithmic graph theory
· Beautifully written for the new mathematician or computer scientist
· Comprehensive treatment ... Read more

Book Description

Customer Reviews (1)

good first text
The book is very typical of Dover books. It gives a reliable, well written discourse on its subject. Berge shows how graph theory can be applied in a variety of fields. His book is suitable for a first course on graph theory, equivalent to one term or semester at the undergraduate level.

The book demonstrates rigour in the proofs, without being entirely strict. So you don't have to wade through theorem after theorem. It could do with sets of exercises.

If the book interests you, consider next a more advanced text by Mollin, "An Introduction to Data Structures and Algorithms". ... Read more

Book Description
Designed for the nonspecialist, this classic text by a world expert is an invaluable reference tool for those interested in a basic understanding of the subject. Exercises, notes and exhaustive references follow each chapter, making it outstanding as both a text and reference for students and researchers in graph theory and its applications. The reader will delight to discover that the topics in this book are coherently unified and include some of the deepest and most beautiful developments in graph theory. ... Read more

Book Description
With a growing range of applications in fields from computer science to chemistry and communications networks, graph theory has enjoyed a rapid increase of interest and widespread recognition as an important area of mathematics. Through more than 20 years of publication, Graphs & Digraphs has remained a popular point of entry to the field, and through its various editions, has evolved with the field from a purely mathematical treatment to one that also addresses the mathematical needs of computer scientists.Carefully updated, streamlined, and enhanced with new features, Graphs & Digraphs, Fourth Edition reflects many of the developments in graph theory that have emerged in recent years. The authors have added discussions on topics of increasing interest, deleted outdated material, and judiciously augmented the Exercises sections to cover a range of problems that reach beyond the construction of proofs.New in the Fourth Edition:· Expanded treatment of Ramsey theory · Major revisions to the material on domination and distance · New material on list colorings that includes interesting recent results · A solutions manual covering many of the exercises available to instructors with qualifying course adoptions · A comprehensive bibliography including an updated list of graph theory booksEvery edition of Graphs & Digraphs has been unique in its reflection the subject as one that is important, intriguing, and most of all beautiful. The fourth edition continues that tradition, offering a comprehensive, tightly integrated, and up-to-date introduction that imparts an appreciation as well as a solid understanding of the material. ... Read more

Customer Reviews (2)

Not enough examples
While I won't argue that the book is thorough and professional, I find it lacking enough examples to let me comprehensively understand the material.In many books, the author will introduce a concept and then give examples to cement the application of these concepts within the chapter text and/or figures.Chartrand and Lesniak use such examples very sparingly, and often for the more mundane concepts that need no additional illustration.In the first few chapters, where a great amount of terminology is introduced, these examples would have been extremely useful to ensure that the reader has a firm grasp on the basics.Instead, I found myself confused in later chapters because I had misunderstood one of the more fundamental concepts.I rarely, if ever, have this problem with a book includes sufficient examples.

While those more versed in graph theory might prefer a book with less example "fluff", someone just getting into the topic really should look elsewhere to ensure themselves a more stable and confident foundation.

Thorough
This was the one book assigned for a class where I did NOT have to go out and buy a few other books in order to round out the assigned text.Chartrand has written books on graph theory directed at students of many different levels, and this one is advanced -- but the keynote attribute ofthis book its thoroughness and accuracy.The proofs depend uponappropriate use of accurate definitions, and here the definitions are VERYclear and specific -- therefore in constructing the proofs in the exercisesthe student really comes to understand the meaning of the definitions andthe concepts they describe.At first I thought this book was going to beunapproachable because it does not kill you with friendly banter, but Ihave come to appreciate its solid approach and trustworthiness not to leadanyone astray mathematically.By the way, graph theory is really fun. Don't pass us the chance to study it! ... Read more