Graph Theory

Name: Graph Theory
Availability: OutOfStock
ISBN: 9783540261834

ISBN-10: 3540261834

ISBN-13: 9783540261834

Edition: 3rd 2006 (Revised)

Authors: Reinhard Diestel

List price: $59.95

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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…

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