Sparsity: graphs, structures, and algorithms
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin ; Heidelberg
Springer
[2012]
|
| Schriftenreihe: | Algorithms and combinatorics
volume 28 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis Inhaltsverzeichnis |
| Beschreibung: | xxiii, 459 Seiten Illustrationen, Diagramme (teilweise farbig) |
| ISBN: | 9783642278747 9783642427763 |
Internformat
MARC
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| 100 | 1 | |a Nešetřil, Jaroslav |d 1946- |e Verfasser |0 (DE-588)13380447X |4 aut | |
| 245 | 1 | 0 | |a Sparsity |b graphs, structures, and algorithms |c Jaroslav Nešetřil ; Patrice Ossona de Mendez |
| 264 | 1 | |a Berlin ; Heidelberg |b Springer |c [2012] | |
| 264 | 4 | |c © 2012 | |
| 300 | |a xxiii, 459 Seiten |b Illustrationen, Diagramme (teilweise farbig) | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Algorithms and combinatorics |v volume 28 | |
| 650 | 0 | 7 | |a Kombinatorische Graphentheorie |0 (DE-588)4164748-8 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Kombinatorische Graphentheorie |0 (DE-588)4164748-8 |D s |
| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Ossona de Mendez, Patrice |d 1966- |e Verfasser |0 (DE-588)1023333708 |4 aut | |
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| 830 | 0 | |a Algorithms and combinatorics |v volume 28 |w (DE-604)BV000617357 |9 28 | |
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-025111976 | ||
Datensatz im Suchindex
| _version_ | 1804149255129006080 |
|---|---|
| adam_text | IMAGE 1
C O N T E N T S
PRESENTATION
1 I N T R O D U C T I O N 3
2 A F E W P R O B L E M S 7
2.1 BREAKING A MESH 7
2.2 FORGING ALLIANCES 9
2.3 ARE SYMMETRIES FREQUENT? 12
2.4 LARGE MATCHINGS ON A TORUS 14
2.5 HOMOMORPHISM DUALITIES 15
T H E T H E O R Y
3 P R O L E G O M E N A 21
3.1 GRAPHS 21
3.2 AVERAGE DEGREE AND MINIMUM DEGREE 22
3.3 GRAPH DEGENERACY AND ORIENTATIONS 23
3.4 GIRTH 27
3.5 MINORS 30
3.6 WIDTH, SEPARATORS AND EXPANDERS 33
3.7 HOMOMORPHISMS 39
3.8 RELATIONAL STRUCTURES AND FIRST-ORDER LOGIC 46
3.9 RAMSEY THEORY 52
3.10 GRAPH PARAMETERS 54
3.11 COMPUTATIONAL COMPLEXITY 56
EXERCISES 59
4 M E A S U R I N G S P A R S I T Y 61
4.1 BASIC DEFINITIONS 61
4.2 SHALLOW MINORS 62
XI
HTTP://D-NB.INFO/1018719369
IMAGE 2
XII CONTENTS
4.3 SHALLOW TOPOLOGICAL MINORS 65
4.4 GRADS AND TOP-GRADS 66
4.5 POLYNOMIAL EQUIVALENCE OF GRADS AND TOP-GRADS 68
4.6 RELATION WITH CHROMATIC NUMBER 77
4.7 STABILITY OF GRADS BY LEXICOGRAPHIC PRODUCT 80
4.8 SHALLOW IMMERSIONS 83
4.9 GENERALIZED COLORING NUMBERS 86
EXERCISES 88
5 C L A S S E S A N D T H E I R C L A S S I F I C A T I O N 89
5.1 OPERATIONS ON CLASSES AND RESOLUTIONS 91
5.2 LOGARITHMIC DENSITY AND CONCENTRATION 97
5.3 CLASSIFICATION OF CLASSES BY CLIQUE MINORS 100
5.4 CLASSIFICATION BY DENSITY-TRICHOTOMY OF CLASSES 102
5.5 CLASSES WITH BOUNDED EXPANSION 104
5.6 CLASSES WITH LOCALLY BOUNDED EXPANSION 107
5.7 A HISTORICAL NOTE ON CONNECTION TO MODEL THEORY 108
5.8 CLASSES OF RELATIONAL STRUCTURES 110
EXERCISES 113
6 B O U N D E D H E I G H T T R E E S A N D T R E E - D E P T H 115
6.1 DEFINITIONS AND BASIC PROPERTIES 115
6.2 TREE-DEPTH, MINORS AND PATHS 117
6.3 COMPACT ELIMINATION TREES AND WEAK-COLORING 122
6.4 TREE-DEPTH, TREE-WIDTH AND VERTEX SEPARATORS 123
6.5 CENTERED COLORINGS 125
6.6 CYCLE RANK 128
6.7 GAMES AND A MIN-MAX FORMULA FOR TREE-DEPTH 130
6.8 REDUCTIONS AND FINITENESS 132
6.9 EHRENFEUCHT-FRAI SSE GAMES 136
6.10 WELL QUASI-ORDERS 136
6.11 T H E HOMOMORPHISM QUASI-ORDER 140
EXERCISES 142
7 D E C O M P O S I T I O N 145
7.1 MOTIVATION, LOW TREE-WIDTH AND LOW TREE-DEPTH 145
7.2 LOW TREE-DEPTH COLORING AND P-CENTERED COLORINGS 153
7.3 TRANSITIVE FRATERNAL AUGMENTATION 154
7.4 FRATERNAL AUGMENTATIONS OF GRAPHS 158
7.5 THE WEAK-COLORING APPROACH 168
EXERCISES 173
IMAGE 3
CONTENTS XIII
8 I N D E P E N D E N C E 175
8.1 HOW WIDE IS A CLASS? 175
8.2 WIDE CLASSES 179
8.3 FINDING D-INDEPENDENT SETS IN GRAPHS 180
8.4 QUASI-WIDE CLASSES 185
8.5 ALMOST WIDE CLASSES 188
8.6 A NICE (ASYMMETRIC) APPLICATION 189
EXERCISES 194
9 F I R S T - O R D E R C S P , L I M I T S A N D H O M O M O R P H I S
M D U A L I T I E S . . . 195
9.1 INTRODUCTION 195
9.2 HOMOMORPHISM DUALITIES AND THE FUNCTOR U 197
9.3 METRICS ON THE HOMOMORPHISM ORDER 203
9.4 LEFT LIMITS AND COUNTABLE STRUCTURES 212
9.5 RIGHT LIMITS AND FULL LIMITS 217
EXERCISES 224
10 P R E S E R V A T I O N T H E O R E M S 227
10.1 INTRODUCTION 227
10.2 PRIMITIVE POSITIVE THEORIES AND LEFT LIMITS 228
10.3 THEORIES AND COUNTABLE STRUCTURES 233
10.4 PRIMITIVE POSITIVE THEORIES AGAIN 235
10.5 QUOTIENT METRIC SPACES 237
10.6 T H E TOPOLOGICAL PRESERVATION THEOREM 240
10.7 HOMOMORPHISM PRESERVATION THEOREMS 242
10.8 HOMOMORPHISM PRESERVATION THEOREMS FOR FINITE STRUCTURES 246
EXERCISES 251
11 R E S T R I C T E D H O M O M O R P H I S M D U A L I T I E S 253
11.1 INTRODUCTION 253
11.2 CLASSES WITH ALL RESTRICTED DUALITIES 254
11.3 CHARACTERIZATION OF CLASSES WITH ALL RESTRICTED DUALITIES BY
DISTANCES 254
11.4 CHARACTERIZATION OF CLASSES WITH ALL RESTRICTED DUALITIES BY LOCAL
HOMOMORPHISMS 256
11.5 RESTRICTED DUALITIES IN BOUNDED EXPANSION CLASSES 260
11.6 CHARACTERIZATION OF CLASSES WITH ALL RESTRICTED DUALITIES BY
REORIENTATIONS 262
11.7 CHARACTERIZATION OF CLASSES WITH ALL RESTRICTED DUALITIES BY
SUBDIVISIONS 264
IMAGE 4
XIV CONTENTS
11.8 FIRST-ORDER DEFINABLE H-COLORINGS 265
11.9 CONSEQUENCES AND RELATED PROBLEMS 269
EXERCISES 274
12 C O U N T I N G 277
12.1 INTRODUCTION 277
12.2 GENERALIZED SUNFLOWERS 281
12.3 COUNTING PATTERNS OF BOUNDED HEIGHT IN A COLORED FOREST . . . 283
12.4 COUNTING IN GRAPHS WITH BOUNDED TREE DEPTH 289
12.5 COUNTING SUBGRAPHS IN GRAPHS 292
12.6 COUNTING SUBGRAPHS IN GRAPHS IN A CLASS 293
EXERCISES 296
13 B A C K T O C L A S S E S 299
13.1 RESOLUTIONS 299
13.2 PARAMETERS 302
13.3 NOWHERE DENSE CLASSES 304
13.4 BOUNDED EXPANSION CLASSES 305
13.5 BOUNDED TREE-DEPTH CLASSES 306
13.6 REMARKS ON STRUCTURES 308
A P P L I C A T I O N S
14 C L A S S E S W I T H B O U N D E D E X P A N S I O N - E X A M P L E
S 313
14.1 RANDOM GRAPHS (ERDOS-RENYI MODEL) 314
14.2 CROSSING NUMBER 319
14.3 QUEUE AND STACK LAYOUTS 321
14.4 QUEUE NUMBER 322
14.5 STACK NUMBER 327
14.6 NON-REPETITIVE COLORINGS 328
EXERCISES 337
15 S O M E A P P L I C A T I O N S 339
15.1 FINDING MATCHING AND PATHS 339
15.2 BURR-ERDOS CONJECTURE 350
15.3 THE GAME CHROMATIC NUMBER 352
15.4 FIEDLER VALUE OF CLASSES WITH SUBLINEAR SEPARATORS 355
16 P R O P E R T Y T E S T I N G , H Y P E R F I N I T E N E S S A N D S
E P A R A T O R S 363
16.1 PROPERTY TESTING 363
16.2 WEAKLY HYPERFINITE CLASSES 368
16.3 VERTEX SEPARATORS 369
16.4 SUB-EXPONENTIAL AI-EXPANSION 373
EXERCISES 379
IMAGE 5
CONTENTS XV
17 C O R E A L G O R I T H M S 381
17.1 DATA STRUCTURES AND ALGORITHMIC ASPECTS 381
17.2 P-TREE-DEPTH COLORING 386
17.3 COMPUTING AND APPROXIMATING TREE-DEPTH 390
17.4 COUNTING HOMOMORPHISMS TO GRAPHS WITH BOUNDED TREE-DEPTH 392
17.5 FIRST-ORDER CORES OF GRAPHS WITH BOUNDED TREE-DEPTH 393 EXERCISES
396
18 A L G O R I T H M I C A P P L I C A T I O N S 397
18.1 INTRODUCTION 397
18.2 TRUNCATED DISTANCES 399
18.3 THE SUBGRAPH ISOMORPHISM PROBLEM AND BOOLEAN QUERIES . . . 400 18.4
THE DISTANCE-D DOMINATING SET PROBLEM 402
18.5 GENERAL FIRST-ORDER MODEL CHECKING 404
18.6 COUNTING VERSIONS OF MODEL CHECKING 407
EXERCISES 410
19 F U R T H E R D I R E C T I O N S 411
20 S O L U T I O N S A N D H I N T S F O R S O M E O F T H E E X E R C I
S E S 417
R E F E R E N C E S 431
I N D E X 451
|
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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 |
| format | Book |
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| id | DE-604.BV040256103 |
| illustrated | Illustrated |
| indexdate | 2024-07-10T00:20:07Z |
| institution | BVB |
| isbn | 9783642278747 9783642427763 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-025111976 |
| oclc_num | 795893513 |
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| owner_facet | DE-11 DE-19 DE-BY-UBM DE-634 DE-188 DE-83 DE-739 DE-473 DE-BY-UBG |
| physical | xxiii, 459 Seiten Illustrationen, Diagramme (teilweise farbig) |
| publishDate | 2012 |
| publishDateSearch | 2012 |
| publishDateSort | 2012 |
| publisher | Springer |
| record_format | marc |
| series | Algorithms and combinatorics |
| series2 | Algorithms and combinatorics |
| spelling | Nešetřil, Jaroslav 1946- Verfasser (DE-588)13380447X aut Sparsity graphs, structures, and algorithms Jaroslav Nešetřil ; Patrice Ossona de Mendez Berlin ; Heidelberg Springer [2012] © 2012 xxiii, 459 Seiten Illustrationen, Diagramme (teilweise farbig) txt rdacontent n rdamedia nc rdacarrier Algorithms and combinatorics volume 28 Kombinatorische Graphentheorie (DE-588)4164748-8 gnd rswk-swf Kombinatorische Graphentheorie (DE-588)4164748-8 s DE-604 Ossona de Mendez, Patrice 1966- Verfasser (DE-588)1023333708 aut Erscheint auch als Online-Ausgabe 978-3-642-27875-4 Algorithms and combinatorics volume 28 (DE-604)BV000617357 28 B:DE-101 application/pdf https://d-nb.info/1018719369/04 Inhaltsverzeichnis DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025111976&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Nešetřil, Jaroslav 1946- Ossona de Mendez, Patrice 1966- Sparsity graphs, structures, and algorithms Algorithms and combinatorics Kombinatorische Graphentheorie (DE-588)4164748-8 gnd |
| subject_GND | (DE-588)4164748-8 |
| title | Sparsity graphs, structures, and algorithms |
| title_auth | Sparsity graphs, structures, and algorithms |
| title_exact_search | Sparsity graphs, structures, and algorithms |
| title_full | Sparsity graphs, structures, and algorithms Jaroslav Nešetřil ; Patrice Ossona de Mendez |
| title_fullStr | Sparsity graphs, structures, and algorithms Jaroslav Nešetřil ; Patrice Ossona de Mendez |
| title_full_unstemmed | Sparsity graphs, structures, and algorithms Jaroslav Nešetřil ; Patrice Ossona de Mendez |
| title_short | Sparsity |
| title_sort | sparsity graphs structures and algorithms |
| title_sub | graphs, structures, and algorithms |
| topic | Kombinatorische Graphentheorie (DE-588)4164748-8 gnd |
| topic_facet | Kombinatorische Graphentheorie |
| url | https://d-nb.info/1018719369/04 http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025111976&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000617357 |
| work_keys_str_mv | AT nesetriljaroslav sparsitygraphsstructuresandalgorithms AT ossonademendezpatrice sparsitygraphsstructuresandalgorithms |
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