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Bibliographic Details
Main Author:	Diestel, Reinhard 1959- (Author)
Format:	Book
Language:	English German
Published:	New York [u.a.] Springer 2000
Edition:	2. ed.
Series:	Graduate texts in mathematics 173
Subjects:	Grafentheorie Graphes, Théorie des Graph theory Graphentheorie Lehrbuch
Online Access:	Inhaltsverzeichnis
Physical Description:	XIV, 312 S. Ill., graph. Darst. : 24 cm
ISBN:	0387950141 0387989765

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MARC


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adam_text	REINHARD DIESTEL GRAPH THEORY SECOND EDITION WITH 122 ILLUSTRATIONS SPRINGER CONTENTS PREFACE VII 1. THE BASICS 1 1.1. GRAPHS 2 1.2. THE DEGREE OF A VERTEX 4 1.3. PATHS AND CYCLES 6 1.4. CONNECTIVITY 9 1.5. TREES AND FORESTS 12 1.6. BIPARTITE GRAPHS 14 1.7. CONTRACTION AND MINORE 16 1.8. EULER TOURS 18 1.9. SOME LINEAR ALGEBRA 20 1.10. OTHER NOTIONS OF GRAPHS 25 EXERCISES 26 NOTES 28 2. MATCHING 29 2.1. MATCHING IN BIPARTITE GRAPHS 29 2.2. MATCHING IN GENERAL GRAPHS 34 2.3. PATH COVERS 39 EXERCISES 40 NOTES 42 XII CONTENTS 3. CONNECTIVITY 43 3.1. 2-CONNECTED GRAPHS AND SUBGRAPHS 43 3.2. THE STRUCTURE OF 3-CONNECTED GRAPHS 45 3.3. MENGER'S THEOREM 50 3.4. MADER'S THEOREM 56 3.5. EDGE-DISJOINT SPANNING TREES 58 3.6. PATHS BETWEEN GIVEN PAIRS OF VERTICES 61 EXERCISES 63 NOTES 65 4. PLANAR GRAPHS 67 4.1. TOPOLOGICAL PREREQUISITES 68 4.2. PLANE GRAPHS 70 4.3. DRAWINGS 76 4.4. PLANAR GRAPHS: KURATOWSKI'S THEOREM 80 4.5. ALGEBRAIC PLANARITY CRITERIA 85 4.6. PLANE DUALITY 87 EXERCISES 89 NOTES 92 5. COLOURING 95 5.1. COLOURING MAPS AND PLANAR GRAPHS 96 5.2. COLOURING VERTICES 98 5.3. COLOURING EDGES 103 5.4. LIST COLOURING 105 5.5. PERFECT GRAPHS 110 EXERCISES 117 NOTES 120 6. FLOWS 123 6.1. CIRCULATIONS 124 6.2. FLOWS IN NETWORKS 125 6.3. GROUP-VALUED FLOWS , 128 6.4. FC-FLOWS FOR SMALL K 133 6.5. FLOW-COLOURING DUALITY 136 6.6. TUTTE'S FLOW CONJECTURES 140 EXERCISES 144 NOTES 145 CONTENTS XUEI 7. SUBSTRUCTURES IN DENSE GRAPHS 147 7.1. SUBGRAPHS 148 7.2. SZEMEREDI'S REGULARITY LEMMA 153 7.3. APPLYING THE REGULARITY LEMMA 160 EXERCISES 165 NOTES 166 8. SUBSTRUCTURES IN SPARSE GRAPHS 169 8.1. TOPOLOGICAL MINORS 170 8.2. MINORE 179 8.3. HADWIGER'S CONJECTURE 181 EXERCISES 184 NOTES 186 9. RAMSEY THEORY FOR GRAPHS 189 9.1. RAMSEY'S ORIGINAL THEOREMS 190 9.2. RAMSEY NUMBERS 193 9.3. INDUCED RAMSEY THEOREMS 197 9.4. RAMSEY PROPERTIES AND CONNECTIVITY 207 EXERCISES 208 NOTES 210 10. HAMILTON CYCLES 213 10.1. SIMPLE SUFFLCIENT CONDITIONS 213 10.2. HAMILTON CYCLES AND DEGREE SEQUENCES 216 10.3. HAMILTON CYCLES IN THE SQUARE OF A GRAPH 218 EXERCISES 226 NOTES 227 11. RANDOM GRAPHS 229 11.1. THE NOTION OF A RANDOM GRAPH 230 11.2. THE PROBABILISTIC METHOD 235 11.3. PROPERTIES OF ALMOST ALL GRAPHS 238 11.4. THRESHOLD FUNCTIONS AND SECOND MOMENTS 242 EXERCISES 247 NOTES 249 XIV CONTENTS 12. MINORS, TREES, AND WQO 251 12.1. WELL-QUASI-ORDERING 251 12.2. THE GRAPH MINOR THEOREM FOR TREES 253 12.3. TREE-DECOMPOSITIONS 255 12.4. TREE-WIDTH AND FORBIDDEN MINORS 263 12.5. THE GRAPH MINOR THEOREM 274 EXERCISES 277 NOTES 280 HINTS FOR ALL THE EXERCISES 283 INDEX 299 SYMBOL INDEX 311
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isbn	0387950141 0387989765
language	English German
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physical	XIV, 312 S. Ill., graph. Darst. : 24 cm
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spelling	Diestel, Reinhard 1959- Verfasser (DE-588)122411986 aut Graphentheorie Graph theory Reinhard Diestel 2. ed. New York [u.a.] Springer 2000 XIV, 312 S. Ill., graph. Darst. : 24 cm txt rdacontent n rdamedia nc rdacarrier Graduate texts in mathematics 173 Grafentheorie gtt Graphes, Théorie des Graph theory Graphentheorie (DE-588)4113782-6 gnd rswk-swf (DE-588)4123623-3 Lehrbuch gnd-content Graphentheorie (DE-588)4113782-6 s DE-604 Graduate texts in mathematics 173 (DE-604)BV000000067 173 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008954748&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis
spellingShingle	Diestel, Reinhard 1959- Graph theory Graduate texts in mathematics Grafentheorie gtt Graphes, Théorie des Graph theory Graphentheorie (DE-588)4113782-6 gnd
subject_GND	(DE-588)4113782-6 (DE-588)4123623-3
title	Graph theory
title_alt	Graphentheorie
title_auth	Graph theory
title_exact_search	Graph theory
title_full	Graph theory Reinhard Diestel
title_fullStr	Graph theory Reinhard Diestel
title_full_unstemmed	Graph theory Reinhard Diestel
title_short	Graph theory
title_sort	graph theory
topic	Grafentheorie gtt Graphes, Théorie des Graph theory Graphentheorie (DE-588)4113782-6 gnd
topic_facet	Grafentheorie Graphes, Théorie des Graph theory Graphentheorie Lehrbuch
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volume_link	(DE-604)BV000000067
work_keys_str_mv	AT diestelreinhard graphentheorie AT diestelreinhard graphtheory

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