Graph Theory

ISBN-10: 3540261834

ISBN-13: 9783540261834

Edition: 3rd 2006 (Revised)

Authors: Reinhard Diestel
List price: $59.95 Buy it from $28.13
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Description: 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. From the reviews of the first two editions (1997, 2000): "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 "The book has received a very enthusiastic reception, which it amply deserves. A masterly elucidation of modern graph theory." Bulletin of the Institute of Combinatorics and its Applications "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

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Book details

List price: $59.95
Edition: 3rd
Copyright year: 2006
Publisher: Springer
Binding: Paperback
Pages: 410
Size: 6.25" wide x 9.25" long x 1.00" tall
Weight: 1.386
Language: English

Preface
The Basics
Graphs
The degree of a vertex
Paths and cycles
Connectivity
Trees and forests
Bipartite graphs
Contraction and minors
Euler tours
Some linear algebra
Other notions of graphs
Exercises
Notes
Matching, Covering and Packing
Matching in bipartite graphs
Matching in general graphs
Packing and covering
Tree-packing and arboricity
Path covers
Exercises
Notes
Connectivity
2-Connected graphs and subgraphs
The structure of 3-connected graphs
Menger's theorem
Mader's theorem
Linking pairs of vertices
Exercises
Notes
Planar Graphs
Topological prerequisites
Plane graphs
Drawings
Planar graphs: Kuratowski's theorem
Algebraic planarity criteria
Plane duality
Exercises
Notes
Colouring
Colouring maps and planar graphs
Colouring vertices
Colouring edges
List colouring
Perfect graphs
Exercises
Notes
Flows
Circulations
Flows in networks
Group-valued flows
k-Flows for small k
Flow-colouring duality
Tutte's flow conjectures
Exercises
Notes
Extremal Graph Theory
Subgraphs
Minors
Hadwiger's conjecture
Szemeredi's regularity lemma
Applying the regularity lemma
Exercises
Notes
Infinite Graphs
Basic notions, facts and techniques
Paths, trees, and ends
Homogeneous and universal graphs
Connectivity and matching
The topological end space
Exercises
Notes
Ramsey Theory for Graphs
Ramsey's original theorems
Ramsey numbers
Induced Ramsey theorems
Ramsey properties and connectivity
Exercises
Notes
Hamilton Cycles
Simple sufficient conditions
Hamilton cycles and degree sequences
Hamilton cycles in the square of a graph
Exercises
Notes
Random Graphs
The notion of a random graph
The probabilistic method
Properties of almost all graphs
Threshold functions and second moments
Exercises
Notes
Minors, Trees and WQO
Well-quasi-ordering
The graph minor theorem for trees
Tree-decompositions
Tree-width and forbidden minors
The graph minor theorem
Exercises
Notes
Infinite sets
Surfaces
Hints for all the exercises
Index
Symbol index
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