Graph theory
著者
書誌事項
Graph theory
（Graduate texts in mathematics, 173）
Springer, 1997
- : hardcover
- : softcover
- タイトル別名
-
Graphentheorie
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注記
Includes index
"This book is a translation of Graphentheorie, Springer-Verlag, 1996"--T.p. verso
内容説明・目次
- 巻冊次
-
: hardcover ISBN 9780387982106
内容説明
This introduction to graph theory offers a reassessment of 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 work seeks to complement, not replace, the existing more algorithmic treatments of the subject. There are examples, illustrations, historical remarks and exercises at the end of each chapter. The text may be used at various levels. It contains all the standard basic material for a first undergraduate course, while it offers more proofs of several more advanced results for a graduate course. These proofs are described in as much detail as their simpler counterparts, with an informal discussion of their underlying ideas complementing their rigorous step-by-step account. Finally, for the professional mathematician the book affords an overview of graph theory, with its typical questions and methods, its classic results.
目次
- The basics
- matching
- connectivity
- planar graphs
- colouring
- flows
- substructures in dense graphs
- substructures in sparse graphs
- Ramsey theory for graphs
- Hamilton cycles
- random graphs
- minors, trees, and WQO.
- 巻冊次
-
: softcover ISBN 9780387982113
内容説明
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.
目次
- The basics
- matching
- connectivity
- planar graphs
- colouring
- flows
- substructures in dense graphs
- substructures in sparse graphs
- Ramsey theory for graphs
- Hamilton cycles
- random graphs
- minors, trees, and WQO.
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