Graph theory serves as a mathematical model for any system involving a binary relation. Partly because of their diagrammatic representation, graphs have an intuitive and aesthetic appeal.
Although there are many results in this field of an elementary nature, there is also an abundance of problems with enough combinatorial sublety to challenge the most sophisticated mathematician.
Earlier versions of this book have been used since 1956 when regular courses on graph theory and combinatorial theory began in the Department of Mathematics at the University of Michigan.
The various topics in the theory of graphs are presented in a logical order, indicating the historical background, and clarifying the exposition by including figures to illustrate concepts and results. In addition, there are three appendices which provide diagrams of graphs, directed graphs, and trees. The emphasis throughout is on theorems rather than algorithms or applications, which however are occasionally mentioned.
Exercises are included throughout the book.
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23 of 26 people found the following review helpful:
4.0 out of 5 stars
A class for theoretical math, but not applied math,
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This review is from: Graph Theory (on Demand Printing Of 02787) (Paperback)
I used this text in school, as a computer science student in a theoretical math class.If you are looking for examples of computer algorithms, look elsewhere; the closest this will get you is to "existence proofs", which is showing that something (such as a hamiltonian cycle) exists in a graph that has thus-and-such number of points or edges, but not tell you which sequence of points/edges make up that something. (For example, a graph can be embedded in a plane unless there's a subgraph that looks like K(5) or K(3,3) inside it - this is in about chapter 5, and an important theorem. The text proves this, but doesn't tell you HOW to embed the graph in a plane.) That said, this is an excellent book for theoretical mathematics. I understand that the first two chapters can be used as a high school math text, as an introduction to proofs, and agree that it would work well. As a formal introduction to proving theorems, especially in a self-contained world (you don't need many prerequisites for this, like you do for a topology or analysis text), this is pretty swell. So, to the person who said that he didn't like this because there weren't algorithms in the book: you can find those in the semiliterate computer science textbooks. (I would insist that the last four words of the previous sentence are redundant.) Look here for mathematics.
12 of 24 people found the following review helpful:
5.0 out of 5 stars
The absolute classic!,
By A Customer
This review is from: Graph Theory (on Demand Printing Of 02787) (Paperback)
This is the abslolute classic in the field and a great introduction to this fascinating area of the discrete mathematics.
3 of 34 people found the following review helpful:
5.0 out of 5 stars
Clasical and Excellent,
By A Customer
This review is from: Graph Theory (on Demand Printing Of 02787) (Paperback)
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