Reinhard Diestel

Graph Theory

• Gebundenes Buch

Produktbeschreibung

The third edition of this standard textbook of modern graph theory has been carefully revised, updated, and substantially extended. Covering all its major recent developments it can be used both as a reliable textbook for an introductory course and as a graduate text: on each topic it covers all the basic material in full detail, and adds one or two deeper results (again with detailed proofs) to illustrate the more advanced methods of that field.

Produktdetails

• Graduate Texts in Mathematics Vol.173
• Verlag: Springer, Berlin
• 3rd ed.
• Seitenzahl: 315
• Erscheinungstermin: 6. Februar 2003
• Englisch
• Abmessung: 245mm
• Gewicht: 750g
• ISBN-13: 9783540261827
• ISBN-10: 3540261826
• Artikelnr.: 07216700

Autorenporträt

Reinhard Diestel, University of Hamburg, Germany

Inhaltsangabe

The Basics.- Matching, Covering and Packing.- Connectivity.- Planar Graphs.- Colouring.- Flows.- External Graph Theory.- Infinite Graphs.- Ramsey Theory for Graphs.- Hamilton Cycles.- Random Graphs.- Minors, Trees, and WQO.- A: Infinite Sets.- B: Surfaces. Preface1: 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 algebra1.10 Other notions of graphsExercisesNotes2: Matching, Covering and Packing2.1 Matching in bipartite graphs 2.2 Matching in general graphs( )2.3 Packing and covering2.4 Tree-packing and arboricity 2.5 Path covers ExercisesNotes3: 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: Flows6.1 Circulations( )6.2 Flows in networks 6.3 Group-valued flows6.4 k-Flows for small k6.5 Flow-colouring duality6.6 Tutte s flow conjecturesExercisesNotes
7: Extremal Graph Theory7.1 Subgraphs 7.2 Minors( ) 7.3 Hadwiger s conjecture 7.4 Szemerédi s regularity lemma7.5 Applying the regularity lemmaExercisesNotes8: Infinite Graphs8.1 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 Notes9: Ramsey Theory for Graphs9.1 Ramsey s original theorems 9.2 Ramsey numbers( )9.3 Induced Ramsey theorems9.4 Ramsey properties and connectivity( )ExercisesNotes10: Hamilton Cycles10.1 Simple sufficient conditions 10.2 Hamilton cycles and degree sequences 10.3 Hamilton cycles in the square of a graphExercisesNotes11: Random Graphs11.1 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 momentsExercisesNotes
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 NotesA. 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.

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The Basics.- Matching Covering and Packing.- Connectivity.- Planar Graphs.- Colouring.- Flows.- Extremal Graph Theory.- Infinite Graphs.- Ramsey Theory for Graphs.- Hamilton Cycles.- Random Graphs.- Graph Minors.

Rezensionen

"RD's attempt provides readers a very valuable and rich learning experience. I will definitely recommend this book to my students and colleagues for knowledge enrichment and advancement." (V. Yegnanarayanan, zbMATH 1375.05002, 2018)
"Graph theory provides a very comprehensive description of different topics in graph theory. This book can definitely be counted as one of the classics in this subject. The highlight is its wide coverage of topics in graph theory, ranging from the fundamentals to very advanced topics. ... The book ranks highly in terms of standards, originality, and class. ... I have no doubt that this book will be a real asset for all graph theorists and those studying graph theory at all levels." (Sudev Naduvath, Computing Reviews, March, 2018)