Reinhard Diestel

Graph Theory

• Broschiertes Buch

Produktbeschreibung

This standard textbook of modern graph theory, now in its fifth edition, combines the authority of a classic with the engaging freshness of style that is the hallmark of active mathematics. It covers the core material of the subject with concise yet reliably complete proofs, while offering glimpses of more advanced methods in each field by one or two deeper results, again with proofs given in full detail.

The book can be used as a reliable text for an introductory course, as a graduate text, and for self-study.

From the reviews:

"This outstanding book cannot be substituted with any other book on the present textbook market. It has every chance of becoming the standard textbook for graph theory." Acta Scientiarum Mathematiciarum

"Deep, clear, wonderful. This is a serious book about the heart of graph theory. It has

depth and integrity." Persi Diaconis & Ron Graham, SIAM Review

"The book hasreceived a very enthusiastic reception, which it amply deserves. A masterly elucidation of modern graph theory."

Bulletin of the Institute of Combinatorics and its Applications
"Succeeds dramatically ... a hell of a good book." MAA Reviews

"A highlight of the book is what is by far the best account in print of the Seymour-Robertson theory of graph minors." Mathematika

" ... like listening to someone explain mathematics." Bulletin of the AMS

Produktdetails

• Graduate Texts in Mathematics 173
• Verlag: Springer / Springer Berlin Heidelberg / Springer, Berlin
• Artikelnr. des Verlages: 978-3-662-57560-4
• 5. Aufl.
• Erscheinungstermin: 5. Juni 2018
• Englisch
• Abmessung: 236mm x 159mm x 28mm
• Gewicht: 710g
• ISBN-13: 9783662575604
• ISBN-10: 3662575604
• Artikelnr.: 52449458

Autorenporträt

Reinhard Diestel is Professor at the Department of Mathematics at the University of Hamburg.

Inhaltsangabe

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.

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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.

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)