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Bibliographic Details
Main Author:	Diestel, Reinhard 1959- (Author)
Format:	Book
Language:	English German
Published:	Berlin [u.a.] Springer 2006
Edition:	3. ed.
Series:	Graduate texts in mathematics 173
Subjects:	Graphes, Théorie des Graph theory Graphentheorie Lehrbuch
Online Access:	Graph theory Inhaltsverzeichnis Inhaltsverzeichnis
Physical Description:	XVI, 410 S. Ill., graph. Darst.
ISBN:	9783540261834 3540261834

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adam_text	REINHARD DIESTEL GRAPH THEORY THIRD EDITION WITH 146 ILLUSTRATIONS 4Y SPRINGER CONTENTS PREFACE VII 1. THE BASICS 1 1.1 GRAPHS* 2 1.2 THE DEGREE OF A VERTEX* 5 1.3 PATHS AND CYCLES* 6 1.4 CONNECTIVITY* 10 1.5 TREES AND FORESTS* 13 1.6 BIPARTITE GRAPHS* 17 1.7 CONTRACTION AND MINORS* 18 1.8 EULER TOURS* 22 1.9 SOME LINEAR ALGEBRA 23 1.10 OTHER NOTIONS OF GRAPHS 28 EXERCISES 30 NOTES 32 2. MATCHING, COVERING AND PACKING 33 2.1 MATCHING IN BIPARTITE GRAPHS* 34 2.2 MATCHING IN GENERAL GRAPHS -* 39 2.3 PACKING AND COVERING 44 2.4 TREE-PACKING AND ARBORICITY 46 2.5 PATH COVERS 49 EXERCISES 51 NOTES 53 * SECTIONS MARKED BY AN ASTERISK ARE RECOMMENDED FOR A FIRST COURSE. OF SECTIONS MARKED (* , THE BEGINNING IS RECOMMENDED FOR A FIRST COURSE. XIV CONTENTS 3. CONNECTIVITY 55 3.1 2-CONNECTED GRAPHS AND SUBGRAPHS* 55 3.2 THE STRUCTURE OF 3-CONNECTED GRAPHS * 57 3.3 MENGER S THEOREM* 62 3.4 MADER S THEOREM 67 3.5 LINKING PAIRS OF VERTICES * 69 EXERCISES 78 NOTES ., 80 4. PLANAR GRAPHS 83 4.1 TOPOLOGICAL PREREQUISITES* 84 4.2 PLANE GRAPHS* 86 4.3 DRAWINGS 92 4.4 PLANAR GRAPHS: KURATOWSKI S THEOREM* 96 4.5 ALGEBRAIC PLANARITY CRITERIA 101 4.6 PLANE DUALITY 103 EXERCISES 106 NOTES 109 5. COLOURING ILL 5.1 COLOURING MAPS AND PLANAR GRAPHS* 112 5.2 COLOURING VERTICES* 114 5.3 COLOURING EDGES* 119 5.4 LIST COLOURING 121 5.5 PERFECT GRAPHS 126 EXERCISES 133 NOTES 136 6. FLOWS 139 6.1 CIRCULATIONS** 140 6.2 FLOWS IN NETWORKS* 141 6.3 GROUP-VALUED FLOWS 144 6.4 FC-FLOWS FOR SMALL K 149 6.5 FLOW-COLOURING DUALITY 152 6.6 TUTTE S FLOW CONJECTURES 156 EXERCISES 160 NOTES 161 CONTENTS XV 7. EXTREMAL GRAPH THEORY 163 7.1 SUBGRAPHS* 164 7.2 MINORS** 169 7.3 HADWIGER S CONJECTURE* 172 7.4 SZEMEREDI S REGULARITY LEMMA 175 7.5 APPLYING THE REGULARITY LEMMA 183 EXERCISES 189 NOTES 192 8. INFINITE GRAPHS 195 8.1 BASIC NOTIONS, FACTS AND TECHNIQUES* 196 8.2 PATHS, TREES, AND ENDS * 204 8.3 HOMOGENEOUS AND UNIVERSAL GRAPHS* 212 8.4 CONNECTIVITY AND MATCHING 216 8.5 THE TOPOLOGICAL END SPACE 226 EXERCISES 237 NOTES 244 9. RAMSEY THEORY FOR GRAPHS 251 9.1 RAMSEY S ORIGINAL THEOREMS* 252 9.2 RAMSEY NUMBERS * 255 9.3 INDUCED RAMSEY THEOREMS 258 9.4 RAMSEY PROPERTIES AND CONNECTIVITY * 268 EXERCISES 271 NOTES 272 10. HAMILTON CYCLES 275 10.1 SIMPLE SUFFICIENT CONDITIONS* 275 10.2 HAMILTON CYCLES AND DEGREE SEQUENCES* 278 10.3 HAMILTON CYCLES IN THE SQUARE OF A GRAPH 281 EXERCISES 289 NOTES 290 XVI CONTENTS 11. RANDOM GRAPHS 293 11.1 THE NOTION OF A RANDOM GRAPH* 294 11.2 THE PROBABILISTIC METHOD* 299 11.3 PROPERTIES OF ALMOST ALL GRAPHS* 302 11.4 THRESHOLD FUNCTIONS AND SECOND MOMENTS 306 EXERCISES 312 NOTES 313 12. MINORS, TREES AND WQO 315 12.1 WELL-QUASI-ORDERING* 316 12.2 THE GRAPH MINOR THEOREM FOR TREES* 317 12.3 TREE-DECOMPOSITIONS 319 12.4 TREE-WIDTH AND FORBIDDEN MINORS 327 12.5 THE GRAPH MINOR THEOREM * 341 EXERCISES 350 NOTES 354 A. INFINITE SETS 357 B. SURFACES 361 HINTS FOR ALL THE EXERCISES 369 INDEX 393 SYMBOL INDEX 409
adam_txt	REINHARD DIESTEL GRAPH THEORY THIRD EDITION WITH 146 ILLUSTRATIONS 4Y SPRINGER CONTENTS PREFACE VII 1. THE BASICS 1 1.1 GRAPHS* 2 1.2 THE DEGREE OF A VERTEX* 5 1.3 PATHS AND CYCLES* 6 1.4 CONNECTIVITY* 10 1.5 TREES AND FORESTS* 13 1.6 BIPARTITE GRAPHS* 17 1.7 CONTRACTION AND MINORS* 18 1.8 EULER TOURS* 22 1.9 SOME LINEAR ALGEBRA 23 1.10 OTHER NOTIONS OF GRAPHS 28 EXERCISES 30 NOTES 32 2. MATCHING, COVERING AND PACKING 33 2.1 MATCHING IN BIPARTITE GRAPHS* 34 2.2 MATCHING IN GENERAL GRAPHS'-' 39 2.3 PACKING AND COVERING 44 2.4 TREE-PACKING AND ARBORICITY 46 2.5 PATH COVERS 49 EXERCISES 51 NOTES 53 SECTIONS MARKED BY AN ASTERISK ARE RECOMMENDED FOR A FIRST COURSE. OF SECTIONS MARKED (', THE BEGINNING IS RECOMMENDED FOR A FIRST COURSE. XIV CONTENTS 3. CONNECTIVITY 55 3.1 2-CONNECTED GRAPHS AND SUBGRAPHS 55 3.2 THE STRUCTURE OF 3-CONNECTED GRAPHS'' 57 3.3 MENGER'S THEOREM 62 3.4 MADER'S THEOREM 67 3.5 LINKING PAIRS OF VERTICES'' 69 EXERCISES 78 NOTES ., 80 4. PLANAR GRAPHS 83 4.1 TOPOLOGICAL PREREQUISITES 84 4.2 PLANE GRAPHS* 86 4.3 DRAWINGS 92 4.4 PLANAR GRAPHS: KURATOWSKI'S THEOREM* 96 4.5 ALGEBRAIC PLANARITY CRITERIA 101 4.6 PLANE DUALITY 103 EXERCISES 106 NOTES 109 5. COLOURING ILL 5.1 COLOURING MAPS AND PLANAR GRAPHS* 112 5.2 COLOURING VERTICES* 114 5.3 COLOURING EDGES* 119 5.4 LIST COLOURING 121 5.5 PERFECT GRAPHS 126 EXERCISES 133 NOTES 136 6. FLOWS 139 6.1 CIRCULATIONS*' 140 6.2 FLOWS IN NETWORKS 141 6.3 GROUP-VALUED FLOWS 144 6.4 FC-FLOWS FOR SMALL K 149 6.5 FLOW-COLOURING DUALITY 152 6.6 TUTTE'S FLOW CONJECTURES 156 EXERCISES 160 NOTES 161 CONTENTS XV 7. EXTREMAL GRAPH THEORY 163 7.1 SUBGRAPHS* 164 7.2 MINORS*' 169 7.3 HADWIGER'S CONJECTURE 172 7.4 SZEMEREDI'S REGULARITY LEMMA 175 7.5 APPLYING THE REGULARITY LEMMA 183 EXERCISES 189 NOTES 192 8. INFINITE GRAPHS 195 8.1 BASIC NOTIONS, FACTS AND TECHNIQUES* 196 8.2 PATHS, TREES, AND ENDS'' 204 8.3 HOMOGENEOUS AND UNIVERSAL GRAPHS 212 8.4 CONNECTIVITY AND MATCHING 216 8.5 THE TOPOLOGICAL END SPACE 226 EXERCISES 237 NOTES 244 9. RAMSEY THEORY FOR GRAPHS 251 9.1 RAMSEY'S ORIGINAL THEOREMS* 252 9.2 RAMSEY NUMBERS'' 255 9.3 INDUCED RAMSEY THEOREMS 258 9.4 RAMSEY PROPERTIES AND CONNECTIVITY'' 268 EXERCISES 271 NOTES 272 10. HAMILTON CYCLES 275 10.1 SIMPLE SUFFICIENT CONDITIONS* 275 10.2 HAMILTON CYCLES AND DEGREE SEQUENCES* 278 10.3 HAMILTON CYCLES IN THE SQUARE OF A GRAPH 281 EXERCISES 289 NOTES 290 XVI CONTENTS 11. RANDOM GRAPHS 293 11.1 THE NOTION OF A RANDOM GRAPH* 294 11.2 THE PROBABILISTIC METHOD* 299 11.3 PROPERTIES OF ALMOST ALL GRAPHS* 302 11.4 THRESHOLD FUNCTIONS AND SECOND MOMENTS 306 EXERCISES 312 NOTES 313 12. MINORS, TREES AND WQO 315 12.1 WELL-QUASI-ORDERING* 316 12.2 THE GRAPH MINOR THEOREM FOR TREES* 317 12.3 TREE-DECOMPOSITIONS 319 12.4 TREE-WIDTH AND FORBIDDEN MINORS 327 12.5 THE GRAPH MINOR THEOREM'*' 341 EXERCISES 350 NOTES 354 A. INFINITE SETS 357 B. SURFACES 361 HINTS FOR ALL THE EXERCISES 369 INDEX 393 SYMBOL INDEX 409
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spelling	Diestel, Reinhard 1959- Verfasser (DE-588)122411986 aut Graphentheorie Graph theory Reinhard Diestel 3. ed. Berlin [u.a.] Springer 2006 XVI, 410 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Graduate texts in mathematics 173 Aus dem Dt. übers. 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 http://digitool.hbz-nrw.de:1801/webclient/DeliveryManager?pid=1515703&custom_att_2=simple_viewer Verlagsdaten Springer Graph theory http://digitool.hbz-nrw.de:1801/webclient/DeliveryManager?pid=1670637&custom_att_2=simple_viewer Graph theory Inhaltsverzeichnis HEBIS Datenaustausch Darmstadt application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016456262&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis
spellingShingle	Diestel, Reinhard 1959- Graph theory Graduate texts in mathematics 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_exact_search_txtP	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	Graphes, Théorie des Graph theory Graphentheorie (DE-588)4113782-6 gnd
topic_facet	Graphes, Théorie des Graph theory Graphentheorie Lehrbuch
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