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Sparsity: graphs, structures, and algorithms

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Bibliographische Detailangaben
Beteiligte Personen:	Nešetřil, Jaroslav 1946- (VerfasserIn), Ossona de Mendez, Patrice 1966- (VerfasserIn)
Format:	Buch
Sprache:	Englisch
Veröffentlicht:	Berlin ; Heidelberg Springer [2012]
Schriftenreihe:	Algorithms and combinatorics volume 28
Schlagwörter:	Kombinatorische Graphentheorie
Links:	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
Umfang:	xxiii, 459 Seiten Illustrationen, Diagramme (teilweise farbig)
ISBN:	9783642278747 9783642427763

Internformat

MARC


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Datensatz im Suchindex

_version_	1819259300555522048
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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author	Nešetřil, Jaroslav 1946- Ossona de Mendez, Patrice 1966-
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id	DE-604.BV040256103
illustrated	Illustrated
indexdate	2024-12-20T16:10:56Z
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	DE-11 DE-19 DE-BY-UBM DE-634 DE-188 DE-83 DE-739 DE-473 DE-BY-UBG
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physical	xxiii, 459 Seiten Illustrationen, Diagramme (teilweise farbig)
publishDate	2012
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publishDateSort	2012
publisher	Springer
record_format	marc
series	Algorithms and combinatorics
series2	Algorithms and combinatorics
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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