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Main Author:	Diestel, Reinhard 1959- (Author)
Format:	Book
Language:	English
Published:	Berlin [u.a.] Springer 2005
Edition:	3. ed.
Series:	Graduate texts in mathematics 173
Subjects:	Graphentheorie - Lehrbuch Graph theory Graphentheorie Lehrbuch
Online Access:	Inhaltstext Inhaltsverzeichnis
Physical Description:	XVI, 410 S. graph. Darst.
ISBN:	9783540261827 3540261826 3540261834

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MARC


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Record in the Search Index

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adam_text	REINHARD DIESTEL GRAPH THEORY THIRD EDITION WITH 146 ILLUSTRATIONS J 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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author	Diestel, Reinhard 1959-
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discipline	Mathematik
edition	3. ed.
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spelling	Diestel, Reinhard 1959- Verfasser (DE-588)122411986 aut Graphentheorie Graph theory Reinhard Diestel 3. ed. Berlin [u.a.] Springer 2005 XVI, 410 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Graduate texts in mathematics 173 Graphentheorie - Lehrbuch 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 text/html http://deposit.dnb.de/cgi-bin/dokserv?id=2647509&prov=M&dok_var=1&dok_ext=htm Inhaltstext HEBIS Datenaustausch Darmstadt application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=013361603&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis
spellingShingle	Diestel, Reinhard 1959- Graph theory Graduate texts in mathematics Graphentheorie - Lehrbuch 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	Graphentheorie - Lehrbuch Graph theory Graphentheorie (DE-588)4113782-6 gnd
topic_facet	Graphentheorie - Lehrbuch Graph theory Graphentheorie Lehrbuch
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