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Janson S., Rucinski A., Luczak T. — Random Graphs
Janson S., Rucinski A., Luczak T. — Random Graphs

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Название: Random Graphs

Авторы: Janson S., Rucinski A., Luczak T.

Аннотация:

Details developments in the theory of random graphs over the past decade, providing a much-needed overview of this area of combinatorics.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2000

Количество страниц: 333

Добавлена в каталог: 18.11.2009

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$\ell$-component      112
0-statement      18
1-Factor      82 89
1-statement      18
2-independent set      88 94
a.a.s.      10
Almost surely      10
Almost surely, asymptotically      10
Analysis of variance      96 241
Arboricity      66
Arithmetic progression      54
Asymptotic equivalence      14
Asymptotic normality      149
Azuma's inequality      37
Bounded in probability      11
Branching process      107
Characteristic function      145
Characteristic function, joint      147
Chebyshev's inequality      8 25 241
Chernoff bound      26
Chernoff's inequality      26
Cherry      82
Chromatic number      106 184
Chromatic number, concentration      187
Closure      282
Coloring algorithm      186
Component, complex      112
Component, giant      104 120
Configuration      235
Configuration, graph      137
Configuration, random      235
Connectivity      104 244
Contiguity      234 264
Convergence in distribution      8
Convergence in probability      8
Copy of graph      7
Copy of graph, induced      77
Copy of graph, isolated      78 157
Copy of graph, nested      219
Copy of graph, solitary      78
Core      105—106 122 124
Cramer — Wold device      9
Cramer's theorem      9
Cumulants      145
Cumulants, mixed      147
Decomposition method      165
Degeneracy number      7 96 184
density      6 64
Density, maximum      6 64
Density, relative      7 222
Dependency graph      11
Diameter      105
diamond      97
Diamond tree      98
Distribution of random graph      1
Distribution, binomial      26
Distribution, determined by moments      140
Distribution, hypergeometric      29
Distribution, lower tail      31
Distribution, upper tail      31 48
Double jump      111
Ehrenhfeucht game      274
Erdoes — Rado arrow notation      196 202
Erdoes — Stone — Simonovits Theorem      205
Evolution      103
Evolutionary path      137
Exact copy      296
Exact copy, separating      296
Exceptional class      213
Excess      112
Expose-and-merge      193
Extension statements      73
Extension, balanced      58
Extension, rooted      282
Extension, vertex      281
Extinction probability      107
First cycle      134
First moment method      54
First-order language      272
FKG inequality      30 58
g-factor      90
G-factor, partial      90
Generating functions      177
Graph functional      162
Graph functional, asymptotically finitely dominated      168
Graph functional, dominated      167
Graph, $K_{1}$-balanced      65
Graph, $K_{2}$-balanced      65
Graph, balanced      58 64
Graph, bounded      215
Graph, cubic      233
Graph, dense      216
Graph, empty      7
Graph, null      7
Graph, order of      6
Graph, p-proportional      172
Graph, regular      233
Graph, size of      6
Graph, strictly $K_{1}$-balanced      65
Graph, strictly $K_{2}$-balanced      65
Graph, strictly balanced      64
Graph, sunshine      203
Graph, uniform      223
Graph, whisk      68 90
Hajnal — Szemeredi theorem      48 94
Half-edge      235
Hall theorem      82
Hall's Condition      82
Hamilton cycles      105 239
Hitting time      19 85
Hoelder's inequality      147
Hypercube      2
Hypercube, spanning      96
Hypergraph      199
Hypergraph, 3-edge-critical      199
Hypergraph, chromatic number of      199
Independence number      179
Isolated subgraphs      79
Isolated trees      80 162
Isolated vertices      80 84 156 161
Juncture      115
Kernel      122
Laplace transform      25
Law of total probability      8
Leader      136
Leading overlap      62 171
Leading overlap, unique      62
Lipschitz condition      38
Log-normal      176
Lollipop graph      71
Mantel's theorem      209—210 224
Markov's inequality      8 25
Martingale      37 127 166 176 247
Martingale, edge exposure      39
Martingale, vertex exposure      39
Matching      7
Median      40
Minimum degree phenomenon      81 105
Moment generating function      25
Moments, Factorial      144
Moments, method of      66 140 237
Monochromatic triangles      209
Neighborhood      7
Neighborhood, closed      7
Pair density      213
Pair density, scaled      212
Partition, edge set      202
Partition, index of      213
Partition, regular      213
Partition, sparsely regular      216
Partition, vertex set      196
Perfect matching      82 105 244 261
Perfect matching, fractional      102
Perfect matching, in hypergraph      100
Persistent model      294
Phase, critical      104
Phase, subcritical      104 112
Phase, supercritical      104 115
Phase, transition      104
Projection, first      162 176
Projection, second      164
Proper edge      281
Property, convex      12
Property, decreasing      12
Property, extremal      208
Property, graph      7 13
Property, increasing      12 261
Property, monotone      12
Property, partition      208
Property, semi-induced      160
Quantifier depth      272
Race of components      136
Ramsey property      1
Ramsey property, edge      202
Ramsey property, nonsymmetric      208
Ramsey property, vertex      196
Random graph      1
Random graph process      4
Random graph process, bipartite      83
Random graph process, continuous      4
Random graph process, restricted      5
Random graph process, the      4 85
Random graph, binomial      2
Random graph, bipartite      2 82
Random graph, distribution of      1
Random graph, evolution      103
Random graph, regular      3 233
Random graph, regular bipartite      241
Random graph, tripartite      226
Random graph, uniform      3
Random hypergraph      100 176 208
Random permutation      205 234 263
Random regular multigraph      235
Random subset      5
Random subset of integers      54 208
Random subset of vertices      48 227
Random subset process      13
Random tournament      3 176
Random variable, indicator      8
Random variable, moments of      140
Random variable, standardized      139
Random variable, zero-one      8
Random variables, negatively related      154
Random variables, positively related      154
Recursive bound behavior      292
Recursive function      289
Regular pair      212
Regular pair, sparsely      216
Regularity Lemma, sparse      215
Regularity Lemma, Szemeredi      213
Reliability network      2
Roof      63
Root      68 281
Rooted graph      68 73 281
Rooted graph, balanced      69 74
Rooted graph, dense      281
Rooted graph, rigid      281
Rooted graph, safe      281
Rooted graph, sparse      281
Rooted graph, strictly balanced      69 74
Scaling factor      212
Second moment method      54 241
Semi-factorial      1'40
Semi-invariants      145
Separability      301
Shamir problem      96
Signature      293
Stability number      7 43 179
Stirling numbers      144
Stirling's formula      113
Subgraph count      67 141 145 150 157 160 164 170 173
Subgraph count, induced      171
Subgraph plot      63
Subgraph, grounded      74
Subgraph, induced      78 7
Subgraph, isolated      79
Subgraph, primal      74
Subgraph, solitary      79
Subgraph, spanned      7
Subgraph, spanning      2
Subgraph, triangle-free      230
SUBPARTITION      213
Subsubsequence principle      12
Suen's inequality      34
Sum scheme      293
Switching theorem      137
Talagrand's Inequality      39
Talagrand's inequality, general form      43
Threshold      18
Threshold, coarse      21
Threshold, sharp      21
Threshold, subgraph containment      55
Threshold, width      21
Total variation distance      153
Trahtenbrot's theorem      303
Triangle-factor      97
Triplet      223
Triplet, exact      223
Turan theorem      76 209
Turan Theorem for random graphs      210
Two-round exposure      6
Vertex degree      7 160
Zero-one law      271
Zero-one law, defect      300
Zero-one law, weak      271 286
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