Modern graph theory:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York [u.a.]
Springer
2002
|
| Edition: | Corr. printing |
| Series: | Graduate texts in mathematics
184 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Hier auch später erschienene, unveränderte Nachdrucke |
| Physical Description: | XIII, 394 S. graph. Darst. |
| ISBN: | 9780387984889 0387984887 0387984917 |
Staff View
MARC
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| 100 | 1 | |a Bollobás, Béla |d 1943- |e Verfasser |0 (DE-588)109481240 |4 aut | |
| 245 | 1 | 0 | |a Modern graph theory |c Béla Bollobás |
| 250 | |a Corr. printing | ||
| 264 | 1 | |a New York [u.a.] |b Springer |c 2002 | |
| 300 | |a XIII, 394 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Graduate texts in mathematics |v 184 | |
| 500 | |a Hier auch später erschienene, unveränderte Nachdrucke | ||
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Record in the Search Index
| _version_ | 1804129441192869888 |
|---|---|
| adam_text | Contents
Apologia
vii
Preface
ix
I Fundamentals I
LI
Definitions
..........................
ł
1.2
Paths, Cycles, and Trees
................... 8
1.3
Hamilton Cycles and
Euler
Circuits
............. 14
1.4
Planar Graphs
......................... 20
1.5
An Application of
Euler
Trails to Algebra
.......... 25
1.6
Exercises
........................... 28
II Electrical Networks
39
ILI
Graphs and Electrical Networks
............... 39
II.2 Squaring the Square
..................... 46
П.З
Vector Spaces and Matrices Associated with Graphs
.... 51
П.4
Exercises
........................... 58
II.5 Notes
............................. 66
III flows, Connectivity and Matching
67
Ш.1
Flows in Directed Graphs
................... 68
Ш.2
Connectivity and Menger s Theorem
............. 73
Ш.З
Matching
........................... 76
Ш.4
Tutte s l-Factor Theorem
................... 82
xii Contents
111.5
Stable Matchings
....................... 85
111.6
Exercises
........................... 91
111.7 Notes............................. 101
IV
Extremal
Problems 103
IV.l
Paths and Cycles
....................... 104
IV.2
Complete Subgraphs.....................
108
IV.3
Hamilton Paths and Cycles
.................. 115
IV.4 The Structure of Graphs
................... 120
rv.5 Szemerédi s
Regularity Lemma
............... 124
IV.6 Simple Applications of
Szemerédi s
Lemma
......... 130
IV.7 Exercises
........................... 135
IV.8 Notes
............................. 142
V Colouring
145
V.I Vertex Colouring
....................... 146
V2 Edge Colouring
........................ 152
V.3 Graphs on Surfaces
...................... 154
V4 List Colouring
........................ 161
V.5 Perfect Graphs
........................ 165
V.6 Exercises
........................... 170
V.7 Notes
............................. 177
VI Ramsey Theory
181
VI,
1
The Fundamental Ramsey Theorems
............. 182
VI.2 Canonical Ramsey Theorems
................. 189
VL3 Ramsey Theory For Graphs
................. 192
VI.4 Ramsey Theory for Integers
................. 197
VI.5 Subsequences
......................... 205
VL6 Exercises
........................... 208
VI.7 Notes
............................. 213
VII
Random Graphs
215
VILI
The Basic Models
—
The Use of the Expectation
....... 216
VII.2 Simple Properties of Almost All Graphs
........... 225
VII.3 Almost Determined Variables
—
The Use of the Variance
. . 228
VII.4 Hamilton Cycles
—
The Use of Graph Theoretic Tools
.... 236
VII.5 The Phase Transition
..................... 240
VIL6 Exercises
........................... 246
VII.7 Notes
............................. 251
VIII
Graphs, Groups and Matrices
253
VIII.1 Cayley and
Schreier
Diagrams
................ 254
VIII.2 The Adjacency Matrix and the Laplacian
.......... 262
VIII.3 Strongly Regular Graphs
................... 270
Contents xiii
VIII.4
Enumeration
and Pólya s
Theorem
.............. 276
VIII.5 Exercises
........................... 283
IX Random Walks on Graphs
295
IX.
1
Electrical Networks Revisited
................ 296
IX.2 Electrical Networks and Random Walks
........... 301
IX.3 Hitting Times and Commute Times
............. 309
IX.4 Conductance and Rapid Mixing
............... 319
IX.5 Exercises
........................... 327
IX.6 Notes
............................. 333
X The
Tutte
Polynomial
335
X.I Basic Properties of the
Tutte
Polynomial
........... 336
X.2 The Universal Form of the
Tutte
Polynomial
......... 340
X.3 The
Tutte
Polynomial in Statistical Mechanics
........ 342
X.4 Special Values of the 1 itte Polynomial
............ 345
X.5 A Spanning Tree Expansion of the
Tutte
Polynomial
.... 350
X.6 Polynomials of Knots and Links
............... 358
X.7 Exercises
........................... 371
X.8 Notes
............................. 377
Symbol Index
379
Name Index
383
Subject Index
387
|
| any_adam_object | 1 |
| author | Bollobás, Béla 1943- |
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| classification_rvk | SK 890 ST 130 |
| ctrlnum | (OCoLC)249371939 (DE-599)BVBBV014693764 |
| 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 15 |
| dewey-tens | 510 - Mathematics |
| discipline | Informatik Mathematik |
| edition | Corr. printing |
| format | Book |
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| id | DE-604.BV014693764 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T19:05:11Z |
| institution | BVB |
| isbn | 9780387984889 0387984887 0387984917 |
| language | English |
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| physical | XIII, 394 S. graph. Darst. |
| publishDate | 2002 |
| publishDateSearch | 2002 |
| publishDateSort | 2002 |
| publisher | Springer |
| record_format | marc |
| series | Graduate texts in mathematics |
| series2 | Graduate texts in mathematics |
| spelling | Bollobás, Béla 1943- Verfasser (DE-588)109481240 aut Modern graph theory Béla Bollobás Corr. printing New York [u.a.] Springer 2002 XIII, 394 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Graduate texts in mathematics 184 Hier auch später erschienene, unveränderte Nachdrucke Graphentheorie - Lehrbuch Graphentheorie (DE-588)4113782-6 gnd rswk-swf 1\p (DE-588)4123623-3 Lehrbuch gnd-content Graphentheorie (DE-588)4113782-6 s DE-604 Graduate texts in mathematics 184 (DE-604)BV000000067 184 Digitalisierung UB Regensburg - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009966003&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- Modern graph theory Graduate texts in mathematics Graphentheorie - Lehrbuch Graphentheorie (DE-588)4113782-6 gnd |
| subject_GND | (DE-588)4113782-6 (DE-588)4123623-3 |
| title | Modern graph theory |
| title_auth | Modern graph theory |
| title_exact_search | Modern graph theory |
| title_full | Modern graph theory Béla Bollobás |
| title_fullStr | Modern graph theory Béla Bollobás |
| title_full_unstemmed | Modern graph theory Béla Bollobás |
| title_short | Modern graph theory |
| title_sort | modern graph theory |
| topic | Graphentheorie - Lehrbuch Graphentheorie (DE-588)4113782-6 gnd |
| topic_facet | Graphentheorie - Lehrbuch Graphentheorie Lehrbuch |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009966003&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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