9783642142789

Graph Theory

by
  • ISBN13:

    9783642142789

  • ISBN10:

    3642142788

  • Edition: 4th
  • Format: Paperback
  • Copyright: 7/29/2010
  • Publisher: Springer Verlag

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Summary

The fourth 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.electronic edition: diestel-graph-theory.comFrom 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

Table of Contents

Prefacep. vii
The Basicsp. 1
Graphs*p. 2
The degree of a vertex*p. 5
Paths and cycles*p. 6
Connectivity*p. 10
Trees and forests*p. 13
Bipartite graphs*p. 17
Contraction and minors*p. 19
Euler tours*p. 22
Some linear algebrap. 23
Other notions of graphsp. 28
Exercisesp. 30
Notesp. 33
Matching Covering and Packingp. 35
Matching in bipartite graphs*p. 36
Matching in general graphs(*)p. 41
Packing and coveringp. 45
Tree-packing and arboricityp. 48
Path coversp. 52
Exercisesp. 54
Notesp. 56
Connectivityp. 59
2-Connected graphs and subgraphs*p. 59
The structure of 3-connected graphs(*)p. 62
Menger's theorem*p. 66
Mader's theoremp. 72
Linking pairs of vertices(*)p. 74
Exercisesp. 82
Notesp. 85
Planar Graphsp. 87
Topological prerequisites*p. 88
Plane graphs*p. 90
Drawingsp. 96
Planar graphs: Kuratowski's theorem*p. 100
Algebraic planarity criteriap. 105
Plane dualityp. 107
Exercisesp. 111
Notesp. 114
Colouringp. 117
Colouring maps and planar graphs*p. 118
Colouring vertices*p. 120
Colouring edges*p. 125
List colouringp. 127
Perfect graphsp. 132
Exercisesp. 139
Notesp. 143
Flowsp. 145
Circulations(*)p. 146
Plows in networks*p. 147
Group-valued flowsp. 150
k-Flows for small kp. 155
Flow-colouring dualityp. 158
Tutte's flow conjecturesp. 161
Exercisesp. 165
Notesp. 167
Extremal Graph Theoryp. 169
Subgraphs*p. 170
Minors(*)p. 175
Hadwiger's conjecture*p. 178
Szemerédi's regularity lemmap. 182
Applying the regularity lemmap. 189
Exercisesp. 195
Notesp. 198
Infinite Graphsp. 203
Basic notions, facts and techniques*p. 204
Paths, trees, and ends(*)p. 213
Homogeneous and universal graphs*p. 222
Connectivity and matchingp. 225
Graphs with ends: the topological viewpointp. 235
Recursive structuresp. 248
Exercisesp. 251
Notesp. 261
Ramsey Theory for Graphsp. 269
Ramsey's original theorems*p. 270
Ramsey numbers(*)p. 273
Induced Ramsey theoremsp. 276
Ramsey properties and connectivity(*)p. 286
Exercisesp. 289
Notesp. 290
Hamilton Cyclesp. 293
Sufficient conditions*p. 293
Hamilton cycles and degree sequences*p. 297
Hamilton cycles in the square of a graphp. 300
Exercisesp. 305
Notesp. 306
Random Graphsp. 309
The notion of a random graph*p. 310
The probabilistic method*p. 315
Properties of almost all graphs*p. 318
Threshold functions and second momentsp. 322
Exercisesp. 329
Notesp. 330
Minors, Trees and WQOp. 333
Well-quasi-ordering*p. 334
The graph minor theorem for trees*p. 335
Tree-decompositionsp. 337
Tree-width and forbidden minorsp. 345
The graph minor theorem(*)p. 359
Exercisesp. 368
Notesp. 373
Infinite setsp. 377
Surfacesp. 383
Hints for all the exercisesp. 391
Indexp. 419
Symbol indexp. 435
Table of Contents provided by Ingram. All Rights Reserved.

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