Graph Theory

An introduction to graph theory. The book aims to offer a reassessment of what are the theory's main fields, methods and results. The theory of finite graphs has developed as a coherent subject in its own right, this book seeks to complement existing more algorithmic treatments of the subject.

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This introduction to graph theory offers a reassessment of what are the theory's main fields, methods and results. Viewed as a branch of pure mathematics, the theory of finite graphs is developed as a coherent subject in its own right, with its own unifying questions and methods. The book thus seeks to complement, not replace, the existing more algorithmic treatments of the subject. Graph theory can be used at various different levels. The book contains all the standard basic material to be taught in a first undergraduate course, complete with detailed proofs and numerous illustrations. To help with the planning of such a course, it includes precise information on the logical dependence of results. For a graduate course, the book offers proofs of several more advanced results. These proofs are described with as much care and detail as their simpler counterparts, often with an informal discussion of their underlying ideas complementing their rigorous step-by-step account.
To the professional mathematician, finally, the book affords an overview of graph theory as it stands at the present: with its typical questions and methods, its classic results, and some of those developments that have occured in this subject.