Graph theory
 Responsibility
 Reinhard Diestel.
 Uniform Title
 Graphentheorie. English
 Edition
 Fifth edition.
 Publication
 Berlin : Springer, [2017]
 Copyright notice
 ©2017
 Physical description
 xviii, 428 pages : illustrations ; 25 cm.
 Series
 Graduate texts in mathematics ; 173.
At the library
Science Library (Li and Ma)
Stacks
Call number  Status 

QA166 .D51413 2017  Unknown 
More options
Description
Creators/Contributors
 Author/Creator
 Diestel, Reinhard, author.
Contents/Summary
 Bibliography
 Includes bibliographical references and index.
 Contents

 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(*)
 The erdőspósa theorem
 Tree packing and arboricity
 Path covers
 Exercises
 Notes
 Connectivity
 2Connected graphs and subgraphs*
 The structure of 3connected 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*
 Groupvalued flows
 kFlows for small k
 Flowcolouring duality
 Tutte's flow conjectures
 Exercises
 Notes
 Extremal Graph Theory
 Subgraphs*
 Minors(*)
 Hadwiger's conjecture*
 Szemerédi'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
 Recursive structures
 Graphs with ends : the complete picture
 The topological cycle space
 Infinite graphs as limits of finite ones
 Exercises
 Notes
 Ramsey Theory for Graphs
 Ramsey's original theorems*
 Ramsey numbers(*)
 Induced Ramsey theorems
 Ramsey properties and connectivity(*)
 Exercises
 Notes
 Hamilton Cycles
 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
 Graph Minors
 Wellquasiordering(*)
 The graph minor theorem for trees
 Treedecompositions(*)
 Treewidth(*)
 Tangles
 Treedecompositions and forbidden minors
 The graph minor theorem(*)
 Exercises
 Notes
 Infinite sets
 Surfaces
 Hints for all the exercises
 Index
 Symbol index.
 Publisher's Summary
 ["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 selfstudy. 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 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 \"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 SeymourRobertson theory of graph minors.\" Mathematika \" ... like listening to someone explain mathematics.\" Bulletin of the AMS.", {"source"=>"(source: Nielsen Book Data)"}, "9783662536216", "20171002"]
Subjects
 Subject
 Graph theory.
Bibliographic information
 Publication date
 2017
 Copyright date
 2017
 Series
 Graduate texts in mathematics ; 173
 ISBN
 3662536218
 9783662536216
 9783662536223 (ebk)
 3662536226 (ebk)