Descriptive complexity, canonisation, and definable graph structure theory:
Gespeichert in:
| 1. Verfasser: | |
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| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Cambridge
Cambridge University Press
2017
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| Schriftenreihe: | Lecture notes in logic
47 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | ix, 543 Seiten Illustrationen, Diagramme 23 cm |
| ISBN: | 9781107014527 |
Internformat
MARC
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Datensatz im Suchindex
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CONTENTS Preface. ix 1. Introduction. Graph minor theory. Treelike decompositions. Descriptive complexity theory. The graph isomorphism problem. The structure of this book. Bibliographical remarks. ί 2 4 6 7 8 11 Chapter 1.1. 1.2. 1.3. 1.4. 1.5. 1.6. Part 1. The basic theory Chapter 2. Background from graph theory and logic. 2.1. General notation. 2.2. Graphs and structures. 2.3. Logics. 2.4. Transductions. 14 14 15 22 32 Chapter 3. Descriptive complexity. 3.1. Logics capturing complexity classes. 3.2. Definable orders. 3.3. Definable
canonisation. 3.4. Finite variable logics and pebble games. 3.5. Isomorphism testing and the Weisfeiler-Leman algorithm. 40 41 51 54 71 79 Chapter 4. Treelike decompositions. 94 4.1. Tree decompositions. 94 4.2. Treelike decompositions. 97 4.3. Normalising treelike decompositions. 104 4.4. Tight decompositions. 110 4.5. Isomorphisms, homomorphisms, and bisimulations. 116 4.6. Tree decompositions and treelike decompositions. 118
vi Chapter 5.1. 5.2. 5.3. 5.4. 5.5. 5.6. Contents 5. Definable decompositions. 123 Decomposition schemes. 123 Normalising definable decompositions. 126 Definable tight decompositions. 128 Lifting definability. 129 Parametrised decomposition schemes. 130 The transitivity lemma. 133 Chapter 6. Graphs of bounded tree WIDTH. 148 6.1. Defining bounded-width decompositions.148 6.2. Defining bounded-width decompositions top-down. 151 Chapter 7. Ordered treelike decompositions. 155 7.1. Definitions and basic results. 155 7.2. Parametrised o-decomposition schemes. 160 7.3. Extension lemmas. 161 7.4. Canonisation via definable ordered treelike decompositions. 166 Chapter 8.1. 8.2. 8.3. 8. 3-connected components. 176 Decomposition into 2-connected components. 176 2-separators of 2-connected graphs. 179 Decomposition
into 3-connected components. 182 Chapter 9. Graphs embeddable in a surface. 189 9.1. Surfaces and embeddings of graphs. 189 9.2. Angles. 204 9.3. Planar graphs. 211 9.4. Graphs on arbitrary surfaces. 218 Part 2. Chapter 10.1. 10.2. 10.3. Definable decompositions of graphs with excluded minors 10. Quasi-4-connected components. 232 Hinges. 232 Decomposition into quasi-4-connected components. 254 The Q4C Lifting Lemma. 264 Chapter 11. Ks-MINOR-FREE graphs. 272 11.1. Decompositions.272 11.2. Definability. 275 Chapter 12.1. 12.2. 12.3. 12.4. 12. Completions of pre-decompositions. 277 Pre-decompositions and completions. 277 Ordered completions. 280 Bounded-width
completions. 281 Derivations of pre-decompositions. 285
Contents 12.5. 12.6. vii The finite extension lemma for ordered completions. 286 The Q4C Completion Lemma. 289 Chapter 13. 13.1. 13.2. 13.3. 13.4. 13.5. Almost planar graphs. 301 Relaxations of planarity. 302 Central vertices. 308 Defining the central faces. 312 Centres and skeletons. 345 Decomposing almost planar graphs and their minors. 349 Chapter 14. 14.1. 14.2. 14.3. 14.4. 14.5. 14.6. Almost planar completions. 361 From almost planar to ordered completions. 361 Grids. 363 Supercentre and superskeleton. 378 The completion theorem for quasi-4-connected graphs. 380 MAPp-star completions. 385 Proof of the Almost Planar Completion Theorem 14.1.3. 390 Chapter 15. Almost-embeddable graphs.393 15.1. Arrangements in a surface. 393 15.2. 15.3. 15.4. 15.5. Shortest path
systems. 407 Simplifying and safe subgraphs.411 Patches.413 Belts. 426 Chapter 16. 16.1. 16.2. 16.3. 16.4. Decompositions of almost-embeddable graphs. 438 The Combination Lemma. 438 The Last Extension Lemma. 445 Decomposing almost-embeddable graphs and their minors . 470 Almost-embeddable completions. 476 Chapter 17. Graphs with excluded minors.487 17.1. The structure of graphs with excluded minors. 487 17.2. The main theorem. 493 Chapter 18. Bits and pieces. 502 18.1. From graphs to relational structures. 502 18.2. Lifting canonisations. 504 18.3. 18.4. Invariant decompositions and canonisation. 511 Directions for further research. 513 Appendix A. Robertson and Seymour’s version of the Local Structure
Theorem. 518 References. 523
viii Contents Symbol index. 531 Index. 535 |
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| indexdate | 2024-11-18T17:01:41Z |
| institution | BVB |
| isbn | 9781107014527 |
| language | English |
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| physical | ix, 543 Seiten Illustrationen, Diagramme 23 cm |
| publishDate | 2017 |
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| publisher | Cambridge University Press |
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| series | Lecture notes in logic |
| series2 | Lecture notes in logic |
| spelling | Grohe, Martin 1967- Verfasser (DE-588)1019542179 aut Descriptive complexity, canonisation, and definable graph structure theory Martin Grohe Cambridge Cambridge University Press 2017 ix, 543 Seiten Illustrationen, Diagramme 23 cm txt rdacontent n rdamedia nc rdacarrier Lecture notes in logic 47 Graphentheorie (DE-588)4113782-6 gnd rswk-swf Logik (DE-588)4036202-4 gnd rswk-swf Graph theory Graphentheorie (DE-588)4113782-6 s Logik (DE-588)4036202-4 s DE-604 Erscheint auch als Online-Ausgabe 9781139028868 Lecture notes in logic 47 (DE-604)BV008909514 47 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=030883145&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Grohe, Martin 1967- Descriptive complexity, canonisation, and definable graph structure theory Lecture notes in logic Graphentheorie (DE-588)4113782-6 gnd Logik (DE-588)4036202-4 gnd |
| subject_GND | (DE-588)4113782-6 (DE-588)4036202-4 |
| title | Descriptive complexity, canonisation, and definable graph structure theory |
| title_auth | Descriptive complexity, canonisation, and definable graph structure theory |
| title_exact_search | Descriptive complexity, canonisation, and definable graph structure theory |
| title_full | Descriptive complexity, canonisation, and definable graph structure theory Martin Grohe |
| title_fullStr | Descriptive complexity, canonisation, and definable graph structure theory Martin Grohe |
| title_full_unstemmed | Descriptive complexity, canonisation, and definable graph structure theory Martin Grohe |
| title_short | Descriptive complexity, canonisation, and definable graph structure theory |
| title_sort | descriptive complexity canonisation and definable graph structure theory |
| topic | Graphentheorie (DE-588)4113782-6 gnd Logik (DE-588)4036202-4 gnd |
| topic_facet | Graphentheorie Logik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=030883145&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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