Random graphs:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Cambridge
Cambridge Univ. Pr.
2008
|
| Ausgabe: | 2. ed. repr. |
| Schriftenreihe: | Cambridge studies in advances mathematics
73 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XVIII, 498 S. |
| ISBN: | 9780521797221 0521797225 |
Internformat
MARC
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| 100 | 1 | |a Bollobás, Béla |d 1943- |e Verfasser |0 (DE-588)109481240 |4 aut | |
| 245 | 1 | 0 | |a Random graphs |c Béla Bollobás |
| 250 | |a 2. ed. repr. | ||
| 264 | 1 | |a Cambridge |b Cambridge Univ. Pr. |c 2008 | |
| 300 | |a XVIII, 498 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Cambridge studies in advances mathematics |v 73 | |
| 650 | 0 | 7 | |a Zufallsgraph |0 (DE-588)4277661-2 |2 gnd |9 rswk-swf |
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Datensatz im Suchindex
| _version_ | 1804143223653793793 |
|---|---|
| adam_text | Contents
Preface
to the Second Edition page
χ
Preface
xi
Notation
xvii
1
Probability Theoretic Preliminaries
1
1.1
Notation and Basic Facts
1
1.2
Some Basic Distributions
5
1.3
Normal Approximation
9
1.4
Inequalities
15
1.5
Convergence in Distribution
25
2
Models of Random Graphs
34
2.1
The Basic Models
34
2.2
Properties of Almost All Graphs
43
2.3
Large Subsets of Vertices
46
2.4
Random Regular Graphs
50
3
The Degree Sequence
60
3.1
The Distribution of an Element of the Degree Sequence
60
3.2
Almost Determined Degrees
65
3.3
The Shape of the Degree Sequence
69
3.4
Jumps and Repeated Values
72
3.5
Fast Algorithms for the Graph Isomorphism Problem
74
4
Small Subgraphs
78
4.1
Strictly Balanced Graphs
79
4.2
Arbitrary Subgraphs
85
4.3
Poisson
Approximation
91
5
The Evolution of Random Graphs
—
Sparse Components
96
5.1
Trees of Given Sizes As Components
96
vu
viii Contents
5.2
The Number of Vertices on Tree Components
102
5.3
The Largest Tree Components
110
5.4
Components Containing Cycles
117
6
The Evolution of Random Graphs
—
the Giant Component
130
6.1
A Gap in the Sequence of Components
130
6.2
The Emergence of the Giant Component
138
6.3
Small Components after Time
и/2
143
6.4
Further Results
148
6.5
Two Applications
153
7
Connectivity and Matchings
160
7.1
The Connectedness of Random Graphs
161
7.2
The fc-Connectedness of Random Graphs
166
7.3
Matchings in Bipartite Graphs
171
7.4
Matchings in Random Graphs
178
7.5
Reliable Networks
189
7.6
Random Regular Graphs
195
8
Long Paths and Cycles
201
8.1
Long Paths in G,./,,
—
First Approach
202
8.2
Hamilton Cycles
—
First Approach
206
8.3
Hamilton Cycles
—
Second Approach
212
8.4
Long Paths in G^
—
Second Approach
219
8.5
Hamilton Cycles in Regular Graphs
—
First Approach
221
8.6
Hamilton Cycles in Regular Graphs
—
Second Approach
224
9
The Automorphism Group
229
9.1
The Number of Unlabelled Graphs
229
9.2
The Asymptotic Number of Unlabelled Regular Graphs
241
9.3
Distinguishing Vertices by Their Distance Sequences
243
9.4
Asymmetric Graphs
245
9.5
Graphs with a Given Automorphism Group
248
10
The Diameter
251
10.1
Large Graphs of Small Diameter
251
10.2
The Diameter of Gp
254
10.3
The Diameter of Random Regular Graphs
264
10.4
Graph Processes
267
10.5
Related Results
271
10.6
Small Worlds
276
11
Cliques, Independent Sets and Colouring
282
11.1
Cliques in Gp
282
Contents ix
11.2
Poisson
Approximation
290
11.3
Greedy Colouring of Random Graphs
294
11.4
The Chromatic Number of Random Graphs
298
11.5
Sparse Graphs
303
12
Ramsey Theory
319
12.1
Bounds on R(s)
320
12.2
Off-Diagonal Ramsey Numbers
324
12.3
Triangle-Free Graphs
332
12.4
Dense Subgraphs
339
12.5
The Size-Ramsey Number of a Path
341
13
Explicit Constructions
348
13.1
Character Sums
348
13.2
The Paley Graph Pq
357
13.3
Dense Graphs
365
13.4
Sparse Graphs
373
13.5
Pseudorandom Graphs
376
14
Sequences, Matrices and Permutations
383
14.1
Random Subgraphs of the Cube
384
14.2
Random Matrices
394
14.3
Balancing Families of Sets
399
14.4
Random Elements of Finite Groups
408
14.5
Random Mappings
412
IS Sorting Algorithms
425
15.1
Finding Most Comparisons in One Round
426
15.2
Sorting in Two Rounds
431
15.3
Sorting with Width
и/2
435
15.4
Bin Packing
442
16
Random Graphs of Small Order
447
16.1
Connectivity
447
16.2
Independent Sets
448
16.3
Colouring
451
16.4
Regular Graphs
455
References
457
Index
496
|
| any_adam_object | 1 |
| author | Bollobás, Béla 1943- |
| author_GND | (DE-588)109481240 |
| author_facet | Bollobás, Béla 1943- |
| author_role | aut |
| author_sort | Bollobás, Béla 1943- |
| author_variant | b b bb |
| building | Verbundindex |
| bvnumber | BV036615989 |
| classification_rvk | SK 820 |
| classification_tum | MAT 055f MAT 602f |
| ctrlnum | (OCoLC)254347548 (DE-599)BVBBV036615989 |
| 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 |
| edition | 2. ed. repr. |
| format | Book |
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| id | DE-604.BV036615989 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T22:44:15Z |
| institution | BVB |
| isbn | 9780521797221 0521797225 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-020536129 |
| oclc_num | 254347548 |
| open_access_boolean | |
| owner | DE-355 DE-BY-UBR DE-11 |
| owner_facet | DE-355 DE-BY-UBR DE-11 |
| physical | XVIII, 498 S. |
| publishDate | 2008 |
| publishDateSearch | 2008 |
| publishDateSort | 2008 |
| publisher | Cambridge Univ. Pr. |
| record_format | marc |
| series | Cambridge studies in advances mathematics |
| series2 | Cambridge studies in advances mathematics |
| spelling | Bollobás, Béla 1943- Verfasser (DE-588)109481240 aut Random graphs Béla Bollobás 2. ed. repr. Cambridge Cambridge Univ. Pr. 2008 XVIII, 498 S. txt rdacontent n rdamedia nc rdacarrier Cambridge studies in advances mathematics 73 Zufallsgraph (DE-588)4277661-2 gnd rswk-swf Mathematische Logik (DE-588)4037951-6 gnd rswk-swf Zufallsgraph (DE-588)4277661-2 s Mathematische Logik (DE-588)4037951-6 s 1\p DE-604 Cambridge studies in advances mathematics 73 (DE-604)BV000003678 73 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020536129&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Bollobás, Béla 1943- Random graphs Cambridge studies in advances mathematics Zufallsgraph (DE-588)4277661-2 gnd Mathematische Logik (DE-588)4037951-6 gnd |
| subject_GND | (DE-588)4277661-2 (DE-588)4037951-6 |
| title | Random graphs |
| title_auth | Random graphs |
| title_exact_search | Random graphs |
| title_full | Random graphs Béla Bollobás |
| title_fullStr | Random graphs Béla Bollobás |
| title_full_unstemmed | Random graphs Béla Bollobás |
| title_short | Random graphs |
| title_sort | random graphs |
| topic | Zufallsgraph (DE-588)4277661-2 gnd Mathematische Logik (DE-588)4037951-6 gnd |
| topic_facet | Zufallsgraph Mathematische Logik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020536129&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000003678 |
| work_keys_str_mv | AT bollobasbela randomgraphs |