Graph theory

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Graph theory / Reinhard Diestel

版:: 2nd ed
資料種別:: 図書
出版情報:: New York : Springer, c2000
形態:: xiv, 312 p. ; 24 cm
シリーズ名:: Graduate texts in mathematics ; 173 <BA00010074>
著者名:: Diestel, Reinhard <DA04688678>
ISBN:: 9780387950143 [0387950141] (: hardcover)
9780387989761 [0387989765] (: softcover)
書誌ID:: BA46398780

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他の版・巻

Graph theory. 4th ed
Reinhard Diestel , Springer , c2010

Graph theory (: hardcover ; : softcover)
Reinhard Diestel , Springer , 1997

書誌詳細

その他の標題:

Graphentheorie

注記:

Includes indexes

主題:

Graph theory

言語:

英語

目次情報:

Preface

The Basics / 1：

Graphs / 1.1：

The degree of a vertex / 1.2：

Paths and cycles / 1.3：

Connectivity / 1.4：

Trees and forests / 1.5：

Bipartite graphs / 1.6：

Contraction and minors / 1 7：

Euler tours / 1.8：

Some linear algebra / 1.9：

Other notions of graphs / 1.10：

Exercises

Notes

Matching, Covering and Packing / 2：

Matching in bipartite graphs / 2.1：

Matching in general graphs(*) / 2.2：

Packing and covering / 2.3：

Tree-packing and arboricity / 2.4：

Path covers / 2.5：

2-Connected graphs and subgraphs / 3：

The structure of 3-connected graphs / 3.2：

Menger's theorem / 3.3：

Mader's theorem / 3.4：

Linking pairs of vertices / 3.5：

Planar Graphs / 4：

Topological prerequisites / 4.1：

Plane graphs / 4.2：

Drawings / 4.3：

Planar graphs: Kuratowski's theorem / 4.4：

Algebraic planarity criteria / 4.5：

Plane duality / 4.6：

Colouring / 5：

Colouring maps and planar graphs / 5.1：

Colouring vertices / 5.2：

Colouring edges / 5.3：

List colouring / 5.4：

Perfect graphs / 5.5：

Flows / 6：

Circulations(*) / 6.1：

Flows in networks / 6.2：

Group-valued flows / 6.3：

k-Flows for small k / 6.4：

Flow-colouring duality / 6.5：

Tutte's flow conjectures / 6.6：

Extremal Graph Theory / 7：

Subgraphs / 7.1：

Minors / 7.2：

Hadwiger's conjecture / 7.3：

SzemerÃ¨di's regularity lemma / 7.4：

Applying the regularity lemma / 7.5：

Infinite Graphs / 8：

Basic notions, facts and techniques / 8.1：

Paths, trees, and ends(*) / 8.2：

Homogeneous and universal graphs / 8.3：

Connectivity and matching / 8.4：

The topological end space / 8.5：

Ramsey Theory for Graphs / 9：

Ramsey's original theorems / 9.1：

Ramsey numbers(*) / 9.2：

Induced Ramsey theorems / 9.3：

Ramsey properties and connectivity / 9.4：

Hamilton Cycles / 10：

Simple sufficient conditions / 10.1：

Hamilton cycles and degree sequences / 10.2：

Hamilton cycles in the square of a graph / 10.3：

Random Graphs / 11：

The notion of a random graph / 11.1：

The probabilistic method / 11.2：

Properties of almost all graphs / 11.3：

Threshold functions and second moments / 11.4：

Minors, Trees and WQO / 12：

Well-quasi-ordering / 12.1：

The graph minor theorem for trees / 12.2：

Tree-decompositions / 12.3：

Tree-width and forbidden minors / 12.4：

The graph minor theorem / 12.5：

A. Infinite sets

B. Surfaces Hints for all the exercises

Index

Symbol index

Sections marked by an asterisk are recommended for a first course

Of sections marked (*), the beginning is recommended for a first course

Preface

The Basics / 1：

Graphs / 1.1：

The degree of a vertex / 1.2：

Paths and cycles / 1.3：

Connectivity / 1.4：

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