Nowhere dense classes of graphs characterisations and algorithmic meta-theorems
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| Format: | Abschlussarbeit Buch |
| Sprache: | English |
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Berlin
Universitätsverlag der TU Berlin
2016
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| Schriftenreihe: | Foundations of computing
5 |
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| 245 | 1 | 0 | |a Nowhere dense classes of graphs |b characterisations and algorithmic meta-theorems |c Sebastian Siebertz |
| 264 | 1 | |a Berlin |b Universitätsverlag der TU Berlin |c 2016 | |
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| 490 | 1 | |a Foundations of computing |v 5 | |
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Datensatz im Suchindex
| _version_ | 1819693456299130880 |
|---|---|
| adam_text | C ONTENTS
INTRODUCTION 1
I. BACKGROUND 9
1. GENERAL BACKGROUND 11
1.1 NUMBERS SETS AND FU N CTION S
.................................................
11
1.2. COMPUTABILITY AND COM
PLEXITY................................................ 12
1.3. STRUCTURES AND ISOM ORP H ISM
S................................................ 15
2. FIRST-ORDER AND MONADIC SECOND ORDER LOG!C 17
2.1 SYNTAX AND SEM ANTICS
.............................................................
17
2.2. SATISFIABILITY AND
MODEL-CHECKING.......................................... 20
2.3 FIRST-ORDER T Y P E S
...................................................................
22
2.4. DEFINABLE INTERPRETATIONS
........................................................
27
2.4.1. DEFINING DISTANCES * THE GAIFMAN GRAPH OF A STRUCTURE 28
2.5. LOCALITY OF FIRST-ORDER L O G I C
.....................................................
30
3. GRAPHS 33
3.1 G RA P H
S........................................................................................
33
3 2 . TREE WIDTH AND FORBIDDEN M IN O R S
......................................... 38
3.3. NOWHERE DENSE CLASSES OF G R A P H S
.......................................... 41
3.4 EVERYTHING IS A (COLOURED)
GRAPH............................................ 45
11* COLOURING
*
COVERING AND PLAYING GAMES 49
4. GENERALISED COLOURING NUMBERS 51
4.1 DEFINITION AND BASIC PROPERTIES
............................................ 52
4.2. A TIGHT BOUND ON BOUNDED TREE WIDTH GRAPHS ........ 55
4.3. BOUNDING THE NUMBERS IN TERMS OF LOW D . . . 59
4.4. A BOUND ON PROPER MINOR CLOSED CLAS^^ ........... 61
4.5. A BOUND IN TERMS OF G E N U S
.....................................................
64
4.6. COMPUTING THE NUMBERS
........................................................
67
5. NEIGHBOURHOOD COVERS 73
*
. THE SPLITTER GAME 79
6.1 THE SPLITTER GAM
E.......................................................................
79
6.2 SOLVING THE INDEPENDENT SET PROB LEM
.................................... 83
I . MODEL-CHECKING 89
7. A RANK PRESERVING LOCALITY THEOREM 93
7.1. FIRST-ORDER LOGIC WITH D ISTN ^ ........... 93
7.2. RANK-PRESERVING LO C A LIT Y
........................................................
97
8. FIRST-ORDER MODEL-CHECKING 109
9. ORDER-INVARIANT MODELCHECKING 113
9.1 SUCCESSOR-AND O
RDER-INVARIANCE.......................................... 114
9.2 MODEL-CHECKING ON ORDERED STRUCTURES ........... 115
9.2.1 SUCCESSOR S TR U C TU R E S
..................................................
115
9.2.2. ORDER R E LA TIO N
.............................................................
118
9.3. MODEL-CHECKING FOR ORDER-INVARIANT MSO-FORMULAS ..... 120
9.4. MODEL-CHECKING FOR SUCCESSOR-INVARIANT FO-FORMULAS . . . 124
10. CONCLUSION AND OPEN PROBLEMS 133
BIBLIOGRAPHY 137
|
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| genre_facet | Hochschulschrift |
| id | DE-604.BV043572560 |
| illustrated | Not Illustrated |
| indexdate | 2024-12-24T05:06:37Z |
| institution | BVB |
| isbn | 9783798328181 9783798328198 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-028987370 |
| oclc_num | 954053819 |
| open_access_boolean | 1 |
| owner | DE-83 DE-634 |
| owner_facet | DE-83 DE-634 |
| physical | xii, 149 Seiten Diagramme |
| psigel | ebook |
| publishDate | 2016 |
| publishDateSearch | 2016 |
| publishDateSort | 2016 |
| publisher | Universitätsverlag der TU Berlin |
| record_format | marc |
| series | Foundations of computing |
| series2 | Foundations of computing |
| spellingShingle | Siebertz, Sebastian Nowhere dense classes of graphs characterisations and algorithmic meta-theorems Foundations of computing Prädikatenlogik (DE-588)4046974-8 gnd Parametrisierte Komplexität (DE-588)4818897-9 gnd Graphentheorie (DE-588)4113782-6 gnd |
| subject_GND | (DE-588)4046974-8 (DE-588)4818897-9 (DE-588)4113782-6 (DE-588)4113937-9 |
| title | Nowhere dense classes of graphs characterisations and algorithmic meta-theorems |
| title_auth | Nowhere dense classes of graphs characterisations and algorithmic meta-theorems |
| title_exact_search | Nowhere dense classes of graphs characterisations and algorithmic meta-theorems |
| title_full | Nowhere dense classes of graphs characterisations and algorithmic meta-theorems Sebastian Siebertz |
| title_fullStr | Nowhere dense classes of graphs characterisations and algorithmic meta-theorems Sebastian Siebertz |
| title_full_unstemmed | Nowhere dense classes of graphs characterisations and algorithmic meta-theorems Sebastian Siebertz |
| title_short | Nowhere dense classes of graphs |
| title_sort | nowhere dense classes of graphs characterisations and algorithmic meta theorems |
| title_sub | characterisations and algorithmic meta-theorems |
| topic | Prädikatenlogik (DE-588)4046974-8 gnd Parametrisierte Komplexität (DE-588)4818897-9 gnd Graphentheorie (DE-588)4113782-6 gnd |
| topic_facet | Prädikatenlogik Parametrisierte Komplexität Graphentheorie Hochschulschrift |
| url | https://doi.org/10.14279/depositonce-5011 http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028987370&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV042337479 |
| work_keys_str_mv | AT siebertzsebastian nowheredenseclassesofgraphscharacterisationsandalgorithmicmetatheorems |