Graph theory:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin [u.a.]
Springer
2005
|
| Ausgabe: | 3. ed. |
| Schriftenreihe: | Graduate texts in mathematics
173 |
| Schlagworte: | |
| Online-Zugang: | Inhaltstext Inhaltsverzeichnis |
| Beschreibung: | XVI, 410 S. graph. Darst. |
| ISBN: | 9783540261827 3540261826 3540261834 |
Internformat
MARC
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Datensatz im Suchindex
| _version_ | 1804133612020301824 |
|---|---|
| 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
|
| any_adam_object | 1 |
| author | Diestel, Reinhard 1959- |
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| callnumber-first | Q - Science |
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| classification_rvk | SK 890 |
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| dewey-full | 511.5 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 511 - General principles of mathematics |
| dewey-raw | 511.5 |
| dewey-search | 511.5 |
| dewey-sort | 3511.5 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 3. ed. |
| format | Book |
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| indexdate | 2024-07-09T20:11:29Z |
| institution | BVB |
| isbn | 9783540261827 3540261826 3540261834 |
| language | English |
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| physical | XVI, 410 S. graph. Darst. |
| publishDate | 2005 |
| publishDateSearch | 2005 |
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| publisher | Springer |
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| series | Graduate texts in mathematics |
| series2 | Graduate texts in mathematics |
| 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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