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El. knyga: Graph Theory

4.07/5 (93 ratings by Goodreads)
  • Formatas: PDF+DRM
  • Serija: Graduate Texts in Mathematics 173
  • Išleidimo metai: 20-Jun-2017
  • Leidėjas: Springer-Verlag Berlin and Heidelberg GmbH & Co. K
  • Kalba: eng
  • ISBN-13: 9783662536223
Kitos knygos pagal šią temą:
Graph TheoryDidesnis paveikslėlis
  • Formatas: PDF+DRM
  • Serija: Graduate Texts in Mathematics 173
  • Išleidimo metai: 20-Jun-2017
  • Leidėjas: Springer-Verlag Berlin and Heidelberg GmbH & Co. K
  • Kalba: eng
  • ISBN-13: 9783662536223
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The fourth edition of this standard textbook of modern graph theory has been revised, updated, and substantially extended. Covering all major recent developments, it can be used both as a reliable textbook for an introductory course and as a graduate text. 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 self-study. 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 Seymour-Robertson theory of graph minors.” Mathematika “ ... like listening to someone explain mathematics.” Bulletin of the AMS

Recenzijos

RDs attempt provides readers a very valuable and rich learning experience. I will definitely recommend this book to my students and colleagues for knowledge enrichment and advancement. (V. Yegnanarayanan, zbMATH 1375.05002, 2018) Graph theory provides a very comprehensive description of different topics in graph theory. This book can definitely be counted as one of the classics in this subject. The highlight is its wide coverage of topics in graph theory, ranging from the fundamentals to very advanced topics. The book ranks highly in terms of standards, originality, and class. I have no doubt that this book will be a real asset for all graph theorists and those studying graph theory at all levels. (Sudev Naduvath, Computing Reviews, March, 2018)

Preface vii
1 The Basics
1(34)
1.1 Graphs*
2(3)
1.2 The degree of a vertex*
5(1)
1.3 Paths and cycles*
6(4)
1.4 Connectivity*
10(3)
1.5 Trees and forests*
13(4)
1.6 Bipartite graphs*
17(2)
1.7 Contraction and minors*
19(3)
1.8 Euler tours*
22(1)
1.9 Some linear algebra
23(4)
1.10 Other notions of graphs
27(8)
Exercises
30(3)
Notes
33(2)
2 Matching, Covering and Packing
35(24)
2.1 Matching in bipartite graphs*
36(5)
2.2 Matching in general graphs(*)
41(4)
2.3 The Erdos-Posa theorem
45(3)
2.4 Tree packing and arboricity
48(4)
2.5 Path covers
52(7)
Exercises
53(3)
Notes
56(3)
3 Connectivity
59(30)
3.1 2-Connected graphs and subgraphs*
59(3)
3.2 The structure of 3-connected graphs(*)
62(5)
3.3 Menger's theorem*
67(5)
3.4 Mader's theorem
72(2)
3.5 Linking pairs of vertices?(*)
74(15)
Exercises
82(3)
Notes
85(4)
4 Planar Graphs
89(30)
4.1 Topological prerequisites*
90(2)
4.2 Plane graphs*
92(6)
4.3 Drawings
98(4)
4.4 Planar graphs: Kuratowski's theorem*
102(5)
4.5 Algebraic planarity criteria
107(3)
4.6 Plane duality
110(9)
Exercises
113(4)
Notes
117(2)
5 Colouring
119(30)
5.1 Colouring maps and planar graphs*
120(2)
5.2 Colouring vertices*
122(5)
5.3 Colouring edges*
127(2)
5.4 List colouring
129(6)
5.5 Perfect graphs
135(14)
Exercises
142(4)
Notes
146(3)
6 Flows
149(24)
6.1 Circulations(*)
150(1)
6.2 Flows in networks*
151(3)
6.3 Group-valued flows
154(5)
6.4 k-Flows for small k
159(3)
6.5 Flow-colouring duality
162(3)
6.6 Tutte's flow conjectures
165(8)
Exercises
169(2)
Notes
171(2)
7 Extremal Graph Theory
173(36)
7.1 Subgraphs*
174(6)
7.2 Minors(*)
180(3)
7.3 Hadwiger's conjecture*
183(4)
7.4 Szemeredi's regularity lemma
187(8)
7.5 Applying the regularity lemma
195(14)
Exercises
201(3)
Notes
204(5)
8 Infinite Graphs
209(74)
8.1 Basic notions, facts and techniques*
210(9)
8.2 Paths, trees, and ends(*)
219(9)
8.3 Homogeneous and universal graphs*
228(3)
8.4 Connectivity and matching
231(11)
8.5 Recursive structures
242(3)
8.6 Graphs with ends: the complete picture
245(9)
8.7 The topological cycle space
254(4)
8.8 Infinite graphs as limits of finite ones
258(25)
Exercises
261(12)
Notes
273(10)
9 Ramsey Theory for Graphs
283(24)
9.1 Ramsey's original theorems*
284(3)
9.2 Ramsey numbers(*)
287(3)
9.3 Induced Ramsey theorems
290(10)
9.4 Ramsey properties and connectivity(*)
300(7)
Exercises
303(1)
Notes
304(3)
10 Hamilton Cycles
307(16)
10.1 Sufficient conditions*
307(4)
10.2 Hamilton cycles and degree sequences
311(3)
10.3 Hamilton cycles in the square of a graph
314(9)
Exercises
319(1)
Notes
320(3)
11 Random Graphs
323(24)
11.1 The notion of a random graph*
324(5)
11.2 The probabilistic method*
329(3)
11.3 Properties of almost all graphs*
332(3)
11.4 Threshold functions and second moments
335(12)
Exercises
342(2)
Notes
344(3)
12 Graph Minors
347(46)
12.1 Well-quasi-ordering(*)
348(1)
12.2 The graph minor theorem for trees
349(2)
12.3 Tree-decompositions(*)
351(4)
12.4 Tree-width(*)
355(5)
12.5 Tangles
360(9)
12.6 Tree-decompositions and forbidden minors
369(5)
12.7 The graph minor theorem(*)
374(19)
Exercises
382(6)
Notes
388(5)
A Infinite sets 393(6)
B Surfaces 399(8)
Hints for all the exercises 407(2)
Index 409(18)
Symbol Index 427
Reinhard Diestel is Professor at the Department of Mathematics at the University of Hamburg.
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