Reinhard Diestel

Graph Theory

Summary

Almost two decades after the appearance of most of the classical texts on the subject, this fresh introduction to Graph Theory offers a reassessment of what are the theory's main fields, methods and results today. 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. It 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, including forward referencing. For a graduate course, the book offers proofs of several more advanced results, most of which thus appear in a book for the first time. 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 today: with its typical questions and methods, its classic results, and some of those developments that have made this subject such an exciting area in recent years.

Contents: Fundamentals; Matching; Connectivity; Planarity; Colouring, Choosability and Perfect Graphs; Flows (network and algebraic); Extremal Graph Theory (including regularity lemma, minors and topological minors); Ramsey Theory; Hamilton Cycles; Random Graphs; Tree-decompositions and Graph Minors

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