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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