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Bollobas B. — Random Graphs
Bollobas B. — Random Graphs



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Название: Random Graphs

Автор: Bollobas B.

Аннотация:

This is a new edition of the now classic text. The already extensive treatment given in the first edition has been heavily revised by the author. The addition of two new sections, numerous new results and 150 references means that this represents an up-to-date and comprehensive account of random graph theory. The theory estimates the number of graphs of a given degree that exhibit certain properties. It not only has numerous combinatorial applications, but also serves as a model for the probabilistic treatment of more complicated random structures. This book, written by an acknowledged expert in the field, can be used by mathematicians, computer scientists and electrical engineers, as well as people working in biomathematics. It is self contained, and with numerous exercises in each chapter, is ideal for advanced courses or self study.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: 2-nd edition

Год издания: 2001

Количество страниц: 498

Добавлена в каталог: 01.03.2007

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$(n, r,\lambda)$-expander graph      374
$\varepsilon$-halved permutation      437
$\varepsilon$-halving algorithm      437
$\varepsilon$-sorted permutation      438
$\varepsilon$-sorting algorithm      438
Acyclic orientation      426
Additional degree      85
Additive character      353
Almost every (a.e.)      36
Alternating inequalities      17
Asymmetric graph      245
Asymptotic performance ratio      442
Average degree      79
Balanced graph      79
Bandwidth      421
Bernoulli r.v.      5
Bin packing algorithm      442
Binomial distribution      5
Boundary      385
Canonical labelling algorithm      74
Cayley graph      366
Ceiling of a number      ix
Central limit theorem      27
CHARACTER      352
Character $\chi$ is of order d      352
Chebyshev’s inequality      2
Chromatic number      296
Circumference      150
CLIQUE      282
Clique number      282
Comparator network      436
Complete matching      160
Complex graph      148
Component      96 133
Concrete random graph      348
Conditional probability      3
Conference graph      246 372
Conference matrix      372
Configuration      52
Consistent orientation      426
Contiguous probability spaces      2
Convergence in distribution      2
Convex property      36
Core      150
Cube, n-dimensional      382
Current path      203
d-step closure      426
d-step implication      426
de Bruijn graph      253
Degree      79
Degree of asymmetry      245
Degree of local asymmetry      245
Degree sequence      60
DeMoivre — Laplace theorem      13
Density function      2
Dependence graph      22
Depth of an algorithm      425
Descendant      439
Diagonal Ramsey number      320
Digraph, random mapping      411
Direct implication      426
Discrepancy      339 399
Distance sequence      244
Distribution function      2
Distribution, binomial      5
Distribution, exponential      7
Distribution, geometric      7
Distribution, hypergeometric      7
Distribution, negative binomial      7
Distribution, normal      9
Distribution, Poisson      8
Dominating number      273
Edge-boundary      385
Edge-revealing martingale      299
Entropy function      373
Excess      148
Expander graph, $(n, r,\lambda)$      374
Expanding graph, (a, b)-      370
Expectation      2
Exponential distribution      7
Expose-and-merge algorithm      302
Factorial moment      3
Field, character of      352
Finite multiset      442
Floor of a number      ix
Fractional part      367
Free loop      150
Function, expectation of      2
Gaussian sum      354
Geometric distribution      7
Giant component      96
Girth of a matroid      194
Grading      85
Graph isomorphism problem      74
Graph process      42
Graph, $(n, r,\lambda)$ expander      374
Graph, (a, b) expanding      370
Graph, additional degree of      85
Graph, asymmetric      245
Graph, average degree of      79
Graph, balanced      79
Graph, Cayley      366
Graph, concrete random      348
Graph, conference      246 372
Graph, de Bruijn      253
Graph, degree of      79
Graph, dependence      22
Graph, discrepancy of      339 399
Graph, grading of      85
Graph, H-      79
Graph, Leland — Solomon      253
Graph, locally connected      200
Graph, Margulis      376
Graph, maximal additional degree of      85
Graph, maximum average degree of      79
Graph, Moore      252
Graph, orientation of      426
Graph, Paley      348 357
Graph, pre-      249
Graph, property of      35
Graph, pseudo-random      348
Graph, quadratic residue      348 357
Graph, r-full      361
Graph, random directed      40
Graph, random mapping      412
Graph, random multi-      77
Graph, random r-regular      50
Graph, random unlabelled      239
Graph, random unweighted      153
Graph, strictly balanced      79
Graph, symmetric      245
Graph, topological H-      317
Greedy algorithm      294
Group, random permutation of      407
H-graph      79
H-graph, topological      317
H-subgraph      79
Hitting radius      170
Hitting time      42 166
Homotopic map      31
Hypergeometric distribution      7
Implication      426
Inclusion-exclusion formula      17
Independence      4
Independence number      273 282
Independence ratio      313
Inequality, alternating      17
Inequality, Chebyshev      2
Inequality, isoperimetric      385
Inequality, Markov      2
Isoperimetric inequality      385
Jumbled graph      377
k-core      150
Kernel of a graph      150
Large component      133
Leland — Solomon graph      253
Lindeberg condition      28
Linearized chord diagram      277
Ljapunov condition      28
Locally connected      200
Loose packing      443
Map, homotopic      31
Map, random      412
Margulis graph      376
Markov’s inequality      2
Matroid, girth of      194
Maximal additional degree      85
Maximum average degree      79
Mean      2
Minimum weight of a spanning tree      153
Moment, nth      2
Monotone increasing property      36
Monotone property      36
Monotone set system      191
Moore bound      252
Moore graph      252
Multigraph, random      77
Multiplicative character      352
Multiset, finite      441
n-dimensional cube      383
Negative binomial distribution      7
Normal distribution      9
nth moment      2
Off-diagonal Ramsey number      320
Order d, for character $\chi$      352
Orientation      426
Packing      442
Pairing      277
Paley graph      348 356
Perfect matching      160
Permutation $\pi\in S_m$ is $\varepsilon$-sorted      438
Phase transition      148
Poisson distribution      8
Pregraph      249
Principal additive character      353
Principal character      352
Probability space      1
Probe      425
Problem of Zarankiewicz      370
Property of a graph      35
Pseudo-random graph      348
Quadratic residue character      352 357
Quadratic residue graph      348 357
Quasi-random graph      380
Question      425
r-dominating number      273
r-dominating set      273
r-full graph      361
r-full tournament      382
r-independence number      273
r-independent set      273
Ramsey number      320
Ramsey theory      319
Random bipartite graph process      171
Random bipartite tournament      94
Random directed graph      40
Random function      412
Random graph process      42
Random greedy algorithm      332
Random map      412
Random mapping digraph      412
Random mapping graph      412
Random multigraph      77
Random permutation      408
Random r-regular graph      50
Random unlabelled graphs      239
Random variable (r.v.)      2
Random weighted graph      153
register      436
Remote pair      259
Remote vertex      259
Restricted bin packing      443
Riemann hypothesis      349
rth factorial moment      3
s-separator      166
Separator      166
Sequence, (n, r)-universal      274
Sequence, packing of      349
Simple transform      206
Small component      133
Spanning tree, minimum weight of      76
Sperner family      394
Sperner Lemma      394
Stirling’s formula      4
Strictly balanced graph      79
Strong rank      395
Super regular graphs      188
Supercritical range      148
Symmetric graph      245
Threshold function      40 418
Topological clique number      317
Topological H-graph      317
Total variation distance      3
transform      206
Transitive closure      426
Uniform colouring      316
Universal sequence      274
Variance      2
Vertex-connectivity      166
Vertex-revealing martingale      298
Width of an algorithm      425
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