Customer Reviews

Schaum's Outline of Graph Theory: Including Hundreds of Solved Problems

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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.

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.

I think the Schaum's Outline, Graph Theory, by V.K. Balakrishanan is a wonderful introduction to graph theory. I decided to write this review after reading some negative reviews of this book. I'm trained in mathematics so I understand that theorems and proofs must be studied carefully and thoughtfully before they make sense. But if one takes the necessary time with this book he or she will come away with a good grasp of the fundamentals of graph theory. Such major topics as connectivity, Hamiltonian graphs, trees, network flows, matching and factors, graph embeddings, and graph coloring are thoroughly covered with carefully worked out problems and proofs. In the chapter on Hamiltonian graphs, for example, we learn about the sequence of theorems by Dirac, Ore, Posa, Bondy, and Chvatal - each one implying its predecessor. The Kruskal and Prim algorithms are covered in the chapter on trees and there is even a mention of matroids here. The max-flow-min-cut theorem by Ford and Fulkerson is derived in the chapter on network flows and from this Menger's theorem is deduced. Tutte's famous theorem on matchings in general graphs is covered in the chapter on matching and factors. The beautiful proof alone by Lovasz of Tutte's theorem is worth the price of the book. Important theorems by Whitney, Konig, Hall, and Dilworth are all here. The chapter on graph coloring has the theorems of Brooks, Vizing, and Heawood, and even a section on reducible graphs and unavoidable sets (which provides the basis for the proof of the Four Color Theorem) What's missing? This book was published in 1997 so there is no mention of the Graph Minor Theorem. But if a student were to master the material in the Schaum's Outline, Graph Theory, he or she would be ready to tackle the Graph Minor Theorem.

This is not to the same standard as most of the books in the Schaum's Outline series. It tries, it has the same format but the author does a very poor job in making it relevant. It is dense almost without point - the examples appear to be perfunctory and you are left asking what is the point of the example.

The other aspect of this book that makes it difficult to read is the method provide for some of the algorithms, then are written in bullet point form not the way you would solve the problem in the real world. Indeed this is probably why the book comes across as an academic exercise rather than a teaching exercise.

There are better books out there and many books on solving graphical equations such as Graph Theory and Its Applications, Second Edition (Discrete Mathematics and Its Applications, Jonathan L. Gross and Jay Yellen actually provide you a more insightful presentation of the topic and as such are far more enlightening than what will be found in these pages.

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 all with great clarity and common reasoning. The outhor gets you enter the subject step by step from the easy problems to the hardest with great skill. Also the algorithms on graphs presented in this book, and in general the algorithmic approach of this book are presented most clearly. You wouldn't leave this book until you'l finish read it and understand graph theory. Finally you would fill that at least on one branch of mathematics you are well sitted.

This book is wonderful in my eyes. However, I do not recommend most Schaum's Outlines as textbooks, but as supplements to texts. They just contain too much. This book is good reference to have if you're doing a course in graph theory or if your work involves graph theory. I highly recommend it for reference use.

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.