Graph theory (Book, 2005) []
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Graph theory

Author: Reinhard Diestel
Publisher: Berlin Heidelberg New York Springer 2005
Series: Graduate texts in mathematics, 173
Edition/Format:   Print book : English : 3. edView all editions and formats

Suitable for an introductory course and as a graduate text, this is a textbook of modern graph theory.


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Genre/Form: Lehrbuch
0 Gesamtdarstellung
Material Type: Internet resource
Document Type: Book, Internet Resource
All Authors / Contributors: Reinhard Diestel
ISBN: 9783540261827 3540261826 3540261834 9783540261834
OCLC Number: 255318383
Description: XVI, 410 S. graph. Darst. 24 cm
Contents: Preface 1: The Basics 1.1 Graphs* 1.2 The degree of a vertex* 1.3 Paths and cycles* 1.4 Connectivity* 1.5 Trees and forests* 1.6 Bipartite graphs* 1 7 Contraction and minors* 1.8 Euler tours* 1.9 Some linear algebra 1.10 Other notions of graphs Exercises Notes 2: Matching, Covering and Packing 2.1 Matching in bipartite graphs* 2.2 Matching in general graphs(*) 2.3 Packing and covering 2.4 Tree-packing and arboricity 2.5 Path covers Exercises Notes 3: Connectivity 3.1 2-Connected graphs and subgraphs* 3.2 The structure of 3-connected graphs(*) 3.3 Menger's theorem* 3.4 Mader's theorem 3.5 Linking pairs of vertices(*) Exercises Notes 4: Planar Graphs 4.1 Topological prerequisites* 4.2 Plane graphs* 4.3 Drawings 4.4 Planar graphs: Kuratowski's theorem* 4.5 Algebraic planarity criteria 4.6 Plane duality Exercises Notes 5: Colouring 5.1 Colouring maps and planar graphs* 5.2 Colouring vertices* 5.3 Colouring edges* 5.4 List colouring 5.5 Perfect graphs Exercises Notes 6: Flows 6.1 Circulations(*) 6.2 Flows in networks* 6.3 Group-valued flows 6.4 k-Flows for small k 6.5 Flow-colouring duality 6.6 Tutte's flow conjectures Exercises Notes 7: Extremal Graph Theory 7.1 Subgraphs* 7.2 Minors(*) 7.3 Hadwiger's conjecture* 7.4 Szemeredi's regularity lemma 7.5 Applying the regularity lemma Exercises Notes 8: Infinite Graphs 8.1 Basic notions, facts and techniques* 8.2 Paths, trees, and ends(*) 8.3 Homogeneous and universal graphs* 8.4 Connectivity and matching 8.5 The topological end space Exercises Notes 9: Ramsey Theory for Graphs 9.1 Ramsey's original theorems* 9.2 Ramsey numbers(*) 9.3 Induced Ramsey theorems 9.4 Ramsey properties and connectivity(*) Exercises Notes 10: Hamilton Cycles 10.1 Simple sufficient conditions* 10.2 Hamilton cycles and degree sequences* 10.3 Hamilton cycles in the square of a graph Exercises Notes 11: Random Graphs 11.1 The notion of a random graph* 11.2 The probabilistic method* 11.3 Properties of almost all graphs* 1 1.4 Threshold functions and second moments Exercises Notes 12: Minors, Trees and WQO 12.1 Well-quasi-ordering* 12.2 The graph minor theorem for trees* 12.3 Tree-decompositions 12.4 Tree-width and forbidden minors 12.5 The graph minor theorem(*) Exercises Notes 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.
Series Title: Graduate texts in mathematics, 173
Responsibility: Reinhard Diestel
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Graph Theory is a very well-written book, now in its third edition and the recipient of the according evolutionary benefits. It succeeds dramatically in its aims, which Diestel gives as "[providing] Read more...

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