Graph theory:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin
Springer
[2017]
|
| Ausgabe: | Fifth edition |
| Schriftenreihe: | Graduate texts in mathematics
173 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis Inhaltsverzeichnis |
| Beschreibung: | xviii, 428 Seiten Illustrationen, Diagramme |
| ISBN: | 9783662536216 9783662571491 3662536218 |
Internformat
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| 100 | 1 | |a Diestel, Reinhard |d 1959- |e Verfasser |0 (DE-588)122411986 |4 aut | |
| 245 | 1 | 0 | |a Graph theory |c Reinhard Diestel |
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| 490 | 1 | |a Graduate texts in mathematics |v 173 | |
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| 653 | |a PBV | ||
| 653 | |a Combinatorics | ||
| 653 | |a Discrete mathematics | ||
| 653 | |a Finite and infinite Graphs | ||
| 653 | |a Graph | ||
| 653 | |a Graph Minors | ||
| 653 | |a Graph theory | ||
| 653 | |a Matching | ||
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Datensatz im Suchindex
| _version_ | 1817967949032456192 |
|---|---|
| adam_text |
Contents Preface. vii 1. The Basics . і 1.1 Graphs* . 1.2 The degree of a vertex* . 2 5 ' 1.3 Paths and cycles* . 1.4 Connectivity* . 6 10 1.5 1.6 1.7 1.8 1.9 Trees and forests* . Bipartite graphs*. Contraction and minors* . Euler tours* . Some linear algebra . 13 17 19 22 23 1.10 Other notions of graphs . 27 Exercises . Notes . 30 33 2. Matching, Coveringand Packing
. 35 2.1 Matching in bipartite graphs* . 2.2 Matching in general graphs^*!. 36 41 2.3 The Erdős-Pósa theorem . 2.4 Tree packing and arboricity. 45 48 2.5 Path covers . Exercises . Notes . 52 53 56 * Sections marked by an asterisk are recommended for a first course. Of sections marked 1*1, the beginning is recommended for a first course.
XVI Contents 3. Connectivity . 3.1 3.2 3.3 3.4 3.5 59 2-Connected graphs and subgraphs* . The structure of З-connected graphs՝**. Menger’s theorem* . Mader’s theorem . Linking pairs of vertices^. Exercises . Notes . 59 62 67 72 74 82 85 4. Planar Graphs . 89 4.1 4.2 4.3 4.4 4.5 4.6 Topological prerequisites* . Plane graphs* . Drawings. Planar graphs: Kuratowski’s theorem* . Algebraic planarity criteria . Plane duality . Exercises
. Notes . 90 92 98 102 107 110 113 117 5. Colouring . 119 5.1 5.2 5.3 5.4 5.5 Colouring maps and planar graphs*. Colouring vertices* . Colouring edges* . List colouring . Perfect graphs. Exercises. Notes . 120 122 127 129 135 142 146 6. Flows . 149 6.1 6.2 6.3 6.4 6.5 6.6 Circulations^. Flows in networks* . Group-valued flows . fc-Flows for small к
. Flow-colouring duality. Tutte’s flow conjectures . Exercises. Notes . 150 151 154 159 162 165 169 171
Contents xvii 7. Extremal Graph Theory . 173 7.1 Subgraphs* . 174 7.2 Minors^*'. 180 7.3 Hadwiger’s conjecture* . 183 7.4 Szemerédi’s regularity lemma . 187 7.5 Applying the regularity lemma . 195 Exercises . 201 Notes . 204 8. Infinite Graphs . 209 8.1 Basic notions, facts and techniques* . 210 8.2 Paths, trees, and ends^*'. 219 8.3 Homogeneous and universal graphs* . 228 8.4 Connectivity and matching . 231 8.5 Recursive structures . 242 8.6 Graphs with ends: the complete picture.245 8.7 The topological cycle space
. 254 8.8 Infinite graphs as limits of finite ones . 258 Exercises. 261 Notes . 273 9. Ramsey Theory for Graphs . 283 9.1 Ramsey’s original theorems* .284 9.2 Ramsey numbers^*'. 287 9.3 Induced Ramsey theorems . 290 9.4 Ramsey properties and connectivity^*'. 300 Exercises. 303 Notes . 304 10. Hamilton Cycles . 307 10.1 Sufficient conditions* . 307 10.2 Hamilton cycles and degree sequences. 311 10.3 Hamilton cycles in the square of a graph . 314 Exercises . 319 Notes
. 320
xviii Contents 11. Random Graphs . 323 11.1 11.2 11.3 11.4 The notion of a random graph* .324 The probabilistic method* .329 Properties of almost all graphs* . 332 Threshold functions and second moments . 335 Exercises . 342 Notes . 344 12. Graph Minors . 347 12.1 Well-quasi-ordering**). 348 12.2 The graph minor theorem for trees . 349 12.3 Tree-decompositions**).351 12.4 12.5 12.6 12.7 Tree-width**). Tangles . Tree-decompositions and forbidden minors . The graph minor theorem**). 355 360 369 374 Exercises
. 382 Notes . 388 A. Infinite sets . 393 B. Surfaces . 399 Hints for all the exercises. 407 Index. 409 Symbol index. 427 |
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| author | Diestel, Reinhard 1959- |
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| author_facet | Diestel, Reinhard 1959- |
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| author_sort | Diestel, Reinhard 1959- |
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| building | Verbundindex |
| bvnumber | BV044001523 |
| classification_rvk | QH 451 SK 890 |
| classification_tum | MAT 055f |
| ctrlnum | (OCoLC)958979490 (DE-599)DNB1113674113 |
| dewey-full | 510 511.5 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 510 - Mathematics 511 - General principles of mathematics |
| dewey-raw | 510 511.5 |
| dewey-search | 510 511.5 |
| dewey-sort | 3510 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik Wirtschaftswissenschaften |
| edition | Fifth edition |
| format | Book |
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| physical | xviii, 428 Seiten Illustrationen, Diagramme |
| publishDate | 2017 |
| publishDateSearch | 2017 |
| publishDateSort | 2017 |
| 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 Graph theory Reinhard Diestel Fifth edition 201702 Berlin Springer [2017] © 2017 xviii, 428 Seiten Illustrationen, Diagramme txt rdacontent n rdamedia nc rdacarrier Graduate texts in mathematics 173 Graphentheorie (DE-588)4113782-6 gnd rswk-swf PBV Combinatorics Discrete mathematics Finite and infinite Graphs Graph Graph Minors Graph theory Matching (DE-588)4123623-3 Lehrbuch gnd-content Graphentheorie (DE-588)4113782-6 s DE-604 Springer-Verlag GmbH (DE-588)1065168780 pbl Erscheint auch als Online-Ausgabe 978-3-662-53622-3 Graduate texts in mathematics 173 (DE-604)BV000000067 173 DE-101 pdf/application http://d-nb.info/1113674113/04 20170804003401 Inhaltsverzeichnis Digitalisierung UB Passau - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029409450&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Diestel, Reinhard 1959- Graph theory Graduate texts in mathematics Graphentheorie (DE-588)4113782-6 gnd |
| subject_GND | (DE-588)4113782-6 (DE-588)4123623-3 |
| title | Graph theory |
| 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 (DE-588)4113782-6 gnd |
| topic_facet | Graphentheorie Lehrbuch |
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