Topics in chromatic graph theory:
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| Other Authors: | , |
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| Format: | Book |
| Language: | English |
| Published: |
Cambridge
Cambridge University Press
2015
|
| Series: | Encyclopedia of mathematics and its applications
156 |
| Subjects: | |
| Online Access: | Cover image Inhaltsverzeichnis |
| Item Description: | Includes bibliographical references |
| Physical Description: | xvi, 370 Seiten Illustrationen |
| ISBN: | 9781107033504 |
Staff View
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Record in the Search Index
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| adam_text | Titel: Topics in chromatic graph theory
Autor: Beineke, Lowell W
Jahr: 2015
Contents
Foreword by Bjarne Toft page xili
Preface xv
Preliminaries 1
LOWELL W. BEINEKE and ROBIN J. WILSON
1. Graph theory 1
2. Graph colourings 9
1 Colouring graphs on surfaces 13
BOJAN MOHAR
1. Introduction 13
2. Planar graphs are 4-colourable and 5-choosable 14
3. Heawood s formula 18
4. Colouring with few colours 20
5. Grotzsch s theorem and its generalizations 23
6. Colouring-flow duality 25
7. The acyclic chromatic number 29
8. Degenerate colourings 30
9. The star chromatic number 31
10. Summary 32
2 Brooks s theorem 36
MICHAEL STIEBITZ and BJARNE TOFT
1. Introduction 36
2. Proofs of Brooks s theorem 37
3. Critical graphs with few edges 41
4. Bounding x by A and co 45
5. Graphs with x close to A 48
6. Notes 50
56
56
57
59
60
64
73
73
74
75
79
81
82
85
86
89
94
94
96
97
101
103
105
108
109
114
114
118
121
128
129
137
137
Contents
Chromatic polynomials
BILL JACKSON
1. Introduction
2. Definitions and elementary properties
3. Log concavity and other inequalities
4. Chromatic roots
5. Related polynomials
Hadwiger s conjecture
KEN-ICHI KAWARABAYASHI
1. Introduction
2. Complete graph minors: early results
3. Contraction-critical graphs
4. Algorithmic aspects of the weak conjecture
5. Algorithmic aspects of the strong conjecture
6. The odd conjecture
7. Independent sets and Hadwiger s conjecture
8. Other variants of the conjecture
9. Open problems
Edge-colourings
JESSICA MCDONALD
1. Introduction
2. Elementary sets and Kempe changes
3. Tashkinov trees and upper bounds
4. Towards the Goldberg-Seymour conjecture
5. Extreme graphs
6. The classification problem and critical graphs
7. The dichotomy of edge-colouring
8. Final thoughts
List-colourings
MICHAEL STIEBITZ and MARGIT VOIGT
1. Introduction
2. Orientations and list-colourings
3. Planar graphs
4. Precolouring extensions
5. Notes
Perfect graphs
NICOLAS TROTIGNON
1. Introduction
Contents
ix
2. Lovasz s perfect graph theorem 139
3. Basic graphs 141
4. Decompositions 142
5. The strategy of the proof 146
6. Book from the Proof 148
7. Recognizing perfect graphs 151
8. Berge trigraphs 152
9. Even pairs: a shorter proof of the SPGT 154
10. Colouring perfect graphs 155
8 Geometric graphs 161
ALEXANDER SOIFER
1. The chromatic number of the plane 161
2. The polychromatic number: lower bounds 162
3. The de Bruijn-Erdos reduction to finite sets 165
4. The polychromatic number: upper bounds 167
5. The continuum of 6-colourings 169
6. Special circumstances 171
7. Space explorations 172
8. Rational spaces 173
9. One odd graph 175
10. Influence of set theory axioms 175
11. Predicting the future 177
9 Integer flows and orientations 181
HONGJIAN LAI, RONG LUO and CUN-QUAN ZHANG
1. Introduction 181
2. Basic properties 183
3. 4-flows 185
4. 3-flows 185
5. 5-flows 187
6. Bounded orientations and circular flows 188
7. Modulo orientations and (2 + l/t)-flows 190
8. Contractible configurations 191
9. Related problems 194
10 Colouring random graphs 199
ROSS J. KANG and COLIN MCDIARMID
1. Introduction 199
2. Dense random graphs 202
3. Sparse random graphs 208
4. Random regular graphs 214
X
Contents
5. Random geometric graphs 217
6. Random planar graphs and related classes 219
7. Other colourings 222
11 Hypergraph colouring 230
CSILLA BUJTAS, ZSOLT TUZA and VTTALY VOLOSHIN
1. Introduction 230
2. Proper vertex- and edge-colourings 234
3. C-colourings 238
4. Colourings of mixed hypergraphs 243
5. Colour-bounded and stably bounded hypergraphs 247
6. Conclusion 251
12 Chromatic scheduling 255
DOMINIQUE DE WERRA and ALAIN HERTZ
1. Introduction 255
2. Colouring with weights on the vertices 256
3. List-colouring 258
4. Mixed graph colouring 260
5. Co-colouring 261
6. Colouring with preferences 262
7. Bandwidth colouring 264
8. Edge-colouring 266
9. Sports scheduling 268
10. Balancing requirements 269
11. Compactness 273
12. Conclusion 274
13 Graph colouring algorithms 277
THORE HUSFELDT
1. Introduction 277
2. Greedy colouring 279
3. Recursion 284
4. Subgraph expansion 287
5. Local augmentation 289
6. Vector colouring 292
7. Reductions 296
8. Conclusion 301
14 Colouring games 304
ZSOLT TUZA and XUDING ZHU
1. Introduction 304
Contents
xi
2. Marking games 307
3. Greedy colouring games 312
4. Playing on the edge-set 312
5. Oriented and directed graphs 313
6. Asymmetric games 315
7. Relaxed games 316
8. Paintability 316
9. Achievement and avoidance games 321
10. The acyclic orientation game 322
15 Unsolved graph colouring problems 327
TOMMY JENSEN and BJARNE TOFT
1. Introduction 327
2. Complete graphs and chromatic numbers 328
3. Graphs on surfaces 333
4. Degrees and colourings 339
5. Edge-colourings 344
6. Flow problems 348
7. Concluding remarks 350
Notes on contributors 358
Index 363
|
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| spelling | Topics in chromatic graph theory edited by Lowell W. Beineke, Robin J. Wilson Cambridge Cambridge University Press 2015 xvi, 370 Seiten Illustrationen txt rdacontent n rdamedia nc rdacarrier Encyclopedia of mathematics and its applications 156 Includes bibliographical references MATHEMATICS / Discrete Mathematics bisacsh Datenverarbeitung Graph coloring Data processing Graph theory Data processing MATHEMATICS / Discrete Mathematics Graphfärbung (DE-588)4472286-2 gnd rswk-swf Graphfärbung (DE-588)4472286-2 s DE-604 Beineke, Lowell W. (DE-588)142229997 edt Wilson, Robin J. 1943- (DE-588)141760176 edt Encyclopedia of mathematics and its applications 156 (DE-604)BV000903719 156 http://assets.cambridge.org/97811070/33504/cover/9781107033504.jpg Cover image HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027796782&sequence=000004&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Topics in chromatic graph theory Encyclopedia of mathematics and its applications MATHEMATICS / Discrete Mathematics bisacsh Datenverarbeitung Graph coloring Data processing Graph theory Data processing MATHEMATICS / Discrete Mathematics Graphfärbung (DE-588)4472286-2 gnd |
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| title | Topics in chromatic graph theory |
| title_auth | Topics in chromatic graph theory |
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| title_short | Topics in chromatic graph theory |
| title_sort | topics in chromatic graph theory |
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