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Main Authors:	Janson, Svante 1955- (Author), Łuczak, Tomasz 1963- (Author), Ruciński, Andrzej 1955- (Author)
Format:	Book
Language:	English
Published:	New York Wiley 2000
Series:	Wiley Interscience series in discrete mathematics and optimization
Subjects:	Zufallsgraph Random graphs
Online Access:	Inhaltsverzeichnis
Physical Description:	XI, 333 S. graph. Darst.
ISBN:	0471175412 9780471175414

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MARC


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adam_text	Contents Preface v 1 Preliminaries 1.1 Models of random graphs 1.2 Notes onnotation and more 1.3 Monotonicity 1.4 Asymptotic equivalence 1.5 Thresholds 1.6 Sharp thresholds 1 1 6 12 14 18 20 2 ExponentiallySmallProbabilities 2.1 Independent summands 2.2 Binomial random subsets 2.3 Suen’s inequality 2.4 Martingales 2.5 Talagrand’s inequality 2.6 The upper tail 25 26 30 34 37 39 48 3 Small Subgraphs 3.1 The containment problem 53 53 ix x CONTENTS 3.2 3.3 3.4 3.5 3.6 Leading overlaps and the subgraph plot Subgraph count at the threshold The covering problem Disjoint copies Variations on the theme Matchings 4-і Perfect matchings 4.2 G-factors 4.3 Two open problems The 5.1 5.2 5.3 5.4 5.5 5.6 5.7 Phase Transition The evolution of the random graph The emergence of the giant component The emergence of the giant: A closer look The structure of the giant component Near the critical period Global properties and the symmetry rule Dynamic properties Asymptotic Distributions 6.1 The method of moments 6.2 Stein’s method: The Poisson case 6.3 Stein’s method: The normal case 6.4 Projections and decompositions 6.5 Further methods The 7.1 7.2 7.3 U 7.5 7.6 Chromatic Number The stability number The chromatic number: A greedy approach The concentration of the chromatic number The chromatic number of dense random graphs The chromatic number of sparse random graphs Vertex partition properties Extremal and Ramsey Properties 8.1 Heuristics and results 8.2 Triangles: The first approach 62 66 68 75 77 81 82 89 96 103 103 107 112 121 126 128 134 139 ЦО 152 157 162 176 179 179 184 187 190 192 196 201 202 209 CONTENTS 8.3 8.4 8.5 The Szemerédi Regularity Lemma A partitiontheorem for random graphs Triangles: An approach with perspective xi 212 216 222 9 Random Regular Graphs 9.1 The configuration model 9.2 Small cycles 9.3 Hamilton cycles 9.4 Proofs 9.5 Contiguity of random regular graphs 9.6 A brief course in contiguity 233 235 236 239 247 256 264 10 Zero-One Laws 10.1 Preliminaries 10.2 Ehrenfeucht games and zero-one laws 10.3 Filling gaps IO.4 Sums of models 10.5 Separability and the speed of convergence 271 271 273 285 292 301 References 307 Index of Notation 327 Index 331
any_adam_object	1
author	Janson, Svante 1955- Łuczak, Tomasz 1963- Ruciński, Andrzej 1955-
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language	English
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spelling	Janson, Svante 1955- Verfasser (DE-588)139272658 aut Random graphs Svante Janson ; Tomasz Luczak ; Andrzej Rucinski New York Wiley 2000 XI, 333 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Wiley Interscience series in discrete mathematics and optimization Zufallsgraph Random graphs Zufallsgraph (DE-588)4277661-2 gnd rswk-swf Zufallsgraph (DE-588)4277661-2 s DE-604 Łuczak, Tomasz 1963- Verfasser (DE-588)139273158 aut Ruciński, Andrzej 1955- Verfasser (DE-588)139273379 aut 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=008888991&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis
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subject_GND	(DE-588)4277661-2
title	Random graphs
title_auth	Random graphs
title_exact_search	Random graphs
title_full	Random graphs Svante Janson ; Tomasz Luczak ; Andrzej Rucinski
title_fullStr	Random graphs Svante Janson ; Tomasz Luczak ; Andrzej Rucinski
title_full_unstemmed	Random graphs Svante Janson ; Tomasz Luczak ; Andrzej Rucinski
title_short	Random graphs
title_sort	random graphs
topic	Zufallsgraph Random graphs Zufallsgraph (DE-588)4277661-2 gnd
topic_facet	Zufallsgraph Random graphs
url	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008888991&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
work_keys_str_mv	AT jansonsvante randomgraphs AT łuczaktomasz randomgraphs AT rucinskiandrzej randomgraphs

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