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Graph Theory (Paperback, 4th)
    ¡¤ ÁöÀºÀÌ | ¿Å±äÀÌ:Reinhard Diestel
    ¡¤ ÃâÆÇ»ç:Springer Verlag
    ¡¤ ÃâÆdz⵵:2010
    ¡¤ Ã¥»óÅÂ:ÃÖ»ó±Þ / 456Á· / 154*234mm / Language: English / ISBN 9783642142789(3642142788)
    ¡¤ ISBN:9783642142789
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    ¡¤ ÆǸŰ¡°Ý : ¿ø
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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.com 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


Preface p. vii
The Basics p. 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 algebra p. 23
Other notions of graphs p. 28
Exercises p. 30
Notes p. 33
Matching Covering and Packing p. 35
Matching in bipartite graphs* p. 36
Matching in general graphs(*) p. 41
Packing and covering p. 45
Tree-packing and arboricity p. 48
Path covers p. 52
Exercises p. 54
Notes p. 56
Connectivity p. 59
2-Connected graphs and subgraphs* p. 59
The structure of 3-connected graphs(*) p. 62
Menger's theorem* p. 66
Mader's theorem p. 72
Linking pairs of vertices(*) p. 74
Exercises p. 82
Notes p. 85
Planar Graphs p. 87
Topological prerequisites* p. 88
Plane graphs* p. 90
Drawings p. 96
Planar graphs: Kuratowski's theorem* p. 100
Algebraic planarity criteria p. 105
Plane duality p. 107
Exercises p. 111
Notes p. 114
Colouring p. 117
Colouring maps and planar graphs* p. 118
Colouring vertices* p. 120
Colouring edges* p. 125
List colouring p. 127
Perfect graphs p. 132
Exercises p. 139
Notes p. 143
Flows p. 145
Circulations(*) p. 146
Plows in networks* p. 147
Group-valued flows p. 150
k-Flows for small k p. 155
Flow-colouring duality p. 158
Tutte's flow conjectures p. 161
Exercises p. 165
Notes p. 167
Extremal Graph Theory p. 169
Subgraphs* p. 170
Minors(*) p. 175
Hadwiger's conjecture* p. 178
Szemer?i's regularity lemma p. 182
Applying the regularity lemma p. 189
Exercises p. 195
Notes p. 198
Infinite Graphs p. 203
Basic notions, facts and techniques* p. 204
Paths, trees, and ends(*) p. 213
Homogeneous and universal graphs* p. 222
Connectivity and matching p. 225
Graphs with ends: the topological viewpoint p. 235
Recursive structures p. 248
Exercises p. 251
Notes p. 261
Ramsey Theory for Graphs p. 269
Ramsey's original theorems* p. 270
Ramsey numbers(*) p. 273
Induced Ramsey theorems p. 276
Ramsey properties and connectivity(*) p. 286
Exercises p. 289
Notes p. 290
Hamilton Cycles p. 293
Sufficient conditions* p. 293
Hamilton cycles and degree sequences* p. 297
Hamilton cycles in the square of a graph p. 300
Exercises p. 305
Notes p. 306
Random Graphs p. 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 moments p. 322
Exercises p. 329
Notes p. 330
Minors, Trees and WQO p. 333
Well-quasi-ordering* p. 334
The graph minor theorem for trees* p. 335
Tree-decompositions p. 337
Tree-width and forbidden minors p. 345
The graph minor theorem(*) p. 359
Exercises p. 368
Notes p. 373
Infinite sets p. 377
Surfaces p. 383
Hints for all the exercises p. 391
Index p. 419
Symbol index p. 435



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