Graph coloring problems:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York, NY [u.a.]
Wiley
1995
|
| Schriftenreihe: | Wiley Interscience Series in Discrete Mathematics and Optimization
A Wiley Interscience Publication |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XIX, 295 Seiten graph. Darst. |
| ISBN: | 0471028657 |
Internformat
MARC
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| 100 | 1 | |a Jensen, Tommy R. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Graph coloring problems |c Tommy R. Jensen, Bjarne Toft, Odense University |
| 264 | 1 | |a New York, NY [u.a.] |b Wiley |c 1995 | |
| 300 | |a XIX, 295 Seiten |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Wiley Interscience Series in Discrete Mathematics and Optimization | |
| 490 | 0 | |a A Wiley Interscience Publication | |
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Datensatz im Suchindex
| _version_ | 1804124774413107200 |
|---|---|
| adam_text | Contents
Preface xv
1 Introduction to Graph Coloring 1
1.1 Basic Definitions 1
1.2 Graphs on Surfaces 3
1.3 Vertex Degrees and Colorings 7
1.4 Criticality and Complexity 8
1.5 Sparse Graphs and Random Graphs 12
1.6 Perfect Graphs 13
1.7 Edge Coloring . 15
1.8 Orientations and Integer Flows 17
1.9 List Coloring 18
1.10 Generalized Graph Coloring 21
1.11 Final Remarks 23
Bibliography 23
2 Planar Graphs 31
2.1 Four Color Theorem 31
2.2 Cartesian Sequences 35
2.3 Intersection Graphs of Planar Segments 36
2.4 Ringel s Earth Moon Problem 36
2.5 Ore and Plummer s Cyclic Chromatic Number 37
2.6 Vertex Partitionings w.r.t. Coloring Number 38
2.7 Vertex Partitionings w.r.t. Maximum Degree 40
2.8 The Three Color Problem 41
2.9 Steinberg s Three Color Problem 42
2.10 Griinbaum and Havel s Three Color Problem 44
2.11 Grotzsch and Sachs Three Color Problem 44
2.12 Barnette s Conjecture 45
2.13 List Coloring Planar Graphs 46
vii
viii Contents
2.14 Kronk and Mitchem s Entire Chromatic Number 47
2.15 Nine Color Conjecture 48
2.16 Uniquely Colorable Graphs 48
2.17 Density of 4 Critical Planar Graphs 49
2.18 Square of Planar Graphs 50
Bibliography 51
3 Graphs on Higher Surfaces 59
3.1 Heawood s Empire Problem 59
3.2 Griinbaum s 3 Edge Color Conjecture 61
3.3 Albertson s Four Color Problem 62
3.4 Improper Colorings 63
3.5 Number of 6 Critical Graphs on a Surface 64
3.6 Toroidal Polyhedra 65
3.7 Polynomial Coloring of Embedded Graphs 66
3.8 Sparse Embedded Graphs 66
3.9 Ringel s 1 Chromatic Number 67
3.10 Borodin s Conjecture on Diagonal Coloring 69
3.11 Acyclic Colorings 69
3.12 Cochromatic Numbers 70
3.13 Graphs on Pseudo Surfaces 70
Bibliography 73
4 Degrees 77
4.1 The Coloring Number 77
4.2 Coloring of Decomposable Graphs 79
4.3 Color Bound Families of Graphs , 80
4.4 Edge Disjoint Placements 81
4.5 Powers of Hamilton Cycles 82
4.6 Brooks Theorem for Triangle Free Graphs 83
4.7 Graphs Without Large Complete Subgraphs 85
4.8 /r Chromatic Graphs of Maximum Degree k 85
4.9 Total Coloring 86
4.10 Equitable Coloring 89
4.11 Acyclic Coloring 89
4.12 Melnikov s Valency Variety Problem 90
4.13 Induced Odd Degree Subgraphs 90
4.14 Strong Chromatic Number 91
Bibliography 92
5 Critical Graphs 97
5.1 Critical Graphs With Many Edges 97
5.2 Minimum Degree of 4 and 5 Critical Graphs 98
Contents jx
5.3 Critical Graphs With Few Edges 99
5.4 Four Critical Amenable Graphs 101
5.5 Four Critical Degree 5 Problem 101
5.6 Large Critical Subgraphs of Critical Graphs 102
5.7 Critical Subgraph Covering a 2 Path 102
5.8 Noninduced Critical Subgraphs 103
5.9 Number of Critical Subgraphs 103
5.10 Subgraphs of Critical Graphs 104
5.11 Minimal Circumference of Critical Graphs 104
5.12 The Erdtts Lovasz Tihany Problem 104
5.13 Partial Joins of Critical Graphs 105
5.14 Vertex Critical Graphs Without Critical Edges 105
Bibliography 106
6 The Conjectures of Hadwiger and Hajos 109
6.1 Hadwiger s Conjecture 109
6.2 Hajos Conjecture 111
6.3 The (m, n) and [m, «] Conjectures 112
6.4 Hadwiger Degree of a Graph 114
6.5 Graphs Without Odd K5 115
6.6 Scheme Conjecture 115
6.7 Chromatic 4 Schemes 116
6.8 Odd Subdivisions of KA 116
6.9 Nonseparating Odd Cycles in 4 Critical Graphs 117
6.10 Minimal Edge Cuts in Contraction Critical Graphs 117
6.11 Kostochka s Conjecture on Hadwiger Number 117
Bibliography 119
7 Sparse Graphs 122
7.1 Blanche Descartes Triangle Free Graphs 122
7.2 Griinbaum s Girth Problem 123
7.3 Smallest Triangle Free fc Chromatic Graphs 123
7.4 Large Bipartite Subgraphs of Triangle Free Graphs 126
7.5 Sparse Subgraphs 126
7.6 Number of Odd Cycle Lengths 127
7.7 Maximum Girth of ^ Chromatic Graphs 127
7.8 Maximum Ratio /a 28
7.9 Chromatic Number of Sparse Random Graphs 128
Bibliography 129
8 Perfect Graphs 131
8.1 Strong Perfect Graph Conjecture 131
8.2 Markosyan s Perfect Graph Problems 132
x Contents
8.3 Bold Conjecture 133
8.4 Raspail (Short Chorded) Graphs 134
8.5 Semistrong Perfect Graph Conjecture 134
8.6 Hoang s Conjecture on 2 Coloring Edges 135
8.7 Neighborhood Perfect Graphs 135
8.8 Monsters 136
8.9 Square Free Berge Graphs 137
8.10 Weakened Strong Perfect Graph Conjecture 138
8.11 GyarfaY Forbidden Subgraph Conjecture 139
8.12 Quasiperfect Graphs 140
8.13 Perfect Graph Recognition 141
8.14 f Perfect Graphs 144
Bibliography 145
9 Geometric and Combinatorial Graphs 150
9.1 Hadwiger Nelson Problem 150
9.2 Ringel s Circle Problem 152
9.3 Sachs Unit Sphere Problem 153
9.4 Sphere Colorings 153
9.5 Graphs of Large Distances 154
9.6 Prime Distance Graphs 155
9.7 Cube Like Graphs 156
9.8 Odd Graph Conjecture 158
9.9 Chord Intersection Graphs 158
9.10 Gyarfas and Lehel s Triangle Free L Graphs 159
9.11 Erdos Faber Lovasz Problem 160
9.12 Alon Saks Seymour Problem 161
9.13 General Kneser Graphs 161
9.14 Question of Gallai Related to Sperner s Lemma 162
Bibliography 163
10 Algorithms 168
10.1 Polynomial Graph Coloring 168
10.2 Polynomial Approximation 169
10.3 Even Chromatic Graphs 169
10.4 Grundy Number 170
10.5 Achromatic Number of a Tree 171
10.6 On Line Coloring 172
10.7 Edge Coloring Multigraphs 174
10.8 Complexity of Directed Graph Coloring 175
10.9 Precedence Constrained 3 Processor Scheduling 176
Bibliography 177
Contents xi
11 Constructions 180
11.1 Direct Product 180
11.2 Wreath Product 181
11.3 A Very Strong Product 182
11.4 Gallai s Problem on Dirac s Construction 183
11.5 Hajos Versus Ore 183
11.6 Length of Hajos Proofs 184
11.7 Hajos Constructions of Critical Graphs 185
11.8 Construction of Hajos Generalized by Dirac 185
11.9 Four Chromaticity in Terms of 3 Colorability 186
Bibliography 187
12 Edge Colorings 190
12.1 Goldberg s Conjecture 190
12.2 Jakobsen s Conjecture 191
12.3 Seymour s r Multigraph Conjecture 192
12.4 Weak Critical Graph Conjecture 192
12.5 Critical Multigraph Conjecture 193
12.6 Vizing s 2 Factor Conjecture 193
12.7 Vizing s Planar Graph Conjecture 193
12.8 Minimal Number of Edges in ^ Critical Graphs 194
12.9 Independent Sets in * Critical Graphs 194
12.10 Hilton s Overfull Subgraph Conjecture 195
12.11 The A Subgraph Conjecture 195
12.12 Regular Graphs of High Degree 196
12.13 Berge and Fulkerson s Conjecture 197
12.14 Petersen Coloring 197
12.15 Tutte s Conjecture on 3 Edge Colorings 198
12.16 Grotzsch and Seymour s Conjecture 199
12.17 Cycle Decomposable 4 Regular Plane Multigraphs 200
12.18 Seymour s Planar 4 Multigraph Conjecture 200
12.19 Uniquely 3 Edge Colorable Planar Graphs 200
12.20 List Edge Chromatic Numbers 201
12.21 Strong Chromatic Index 202
12.22 Vizing s Interchange Problem 203
12.23 Scheduling Without Waiting Periods 203
Bibliography 205
13 Orientations and Flows 209
13.1 Tutte s 5 Flow Conjecture 209
13.2 Tutte s 4 Flow Conjecture 210
13.3 Tutte s 3 Flow Conjecture 212
13.4 Bouchet s 6 Flow Conjecture 213
xii Contents
13.5 Jaeger s Circular Flow Conjecture 213
13.6 Berge s Strong Path Partition Conjecture 214
13.7 Berge s Directed Path Conjecture 214
13.8 Minimal Orientations of Critical Graphs 215
13.9 Alon Tarsi Orientations and Chromatic Number 216
Bibliography 218
14 Chromatic Polynomials 220
14.1 Coefficients of Chromatic Polynomials 220
14.2 Characterization of Chromatic Polynomials 221
14.3 Chromatic Uniqueness 221
14.4 Chromatic Equivalence 223
14.5 Zeros of Chromatic Polynomials 225
14.6 Beraha Conjecture 226
14.7 Chessboard Problem 226
14.8 Coefficients for Hypergraphs 227
Bibliography 227
15 Hypergraphs 231
15.1 Erdos Property B 231
15.2 Property B(s) 232
15.3 Finite Projective Planes 233
15.4 Steiner Triple Systems 234
15.5 Steiner Quadruple Systems 235
15.6 Minimum Weight 3 Chromatic Hypergraphs 235
15.7 Positional Games 236
15.8 Tic Tac Toe 237
15.9 Square Hypergraphs 239
15.10 Size of 3 Chromatic Uniform Cliques 241
15.11 Monochromatic Sum Sets 241
15.12 Arithmetic Progressions 242
15.13 Unprovability 243
15.14 The Direct Product of Hypergraphs 244
15.15 Maximal Complete Subgraphs in Perfect Graphs 244
15.16 Coloring Triangulable Manifolds 245
15.17 Berge s Conjecture on Edge Coloring 246
Bibliography 247
16 Infinite Chromatic Graphs 251
16.1 Sparse Subgraphs of High Chromatic Number 251
16.2 Infinite Chromatic Subgraphs 252
16.3 Almost Bipartite Subgraphs 252
16.4 Large Finite n Chromatic Subgraphs 253
Contents xiii
16.5 Trees in Triangle Free Graphs 253
16.6 Unavoidable Classes of Finite Subgraphs 254
16.7 4 Chromatic Subgraphs 254
16.8 Avoiding 5 Cycles and Large Bipartite Subgraphs 255
16.9 Connectivity of Subgraphs 255
16.10 Set of Odd Cycle Lengths 255
16.11 Unavoidable Cycle Lengths 256
16.12 Coloring Number 257
16.13 Direct Product 257
16.14 Partition Problem of Galvin and Hajnal 258
16.15 Small Subgraphs of Large Chromatic Number 258
Bibliography 259
17 Miscellaneous Problems 261
17.1 List Coloring Bipartite Graphs 261
17.2 List Coloring the Union of Graphs 262
17.3 Cochromatic Number 262
17.4 Star Chromatic Number 263
17.5 Harmonious Chromatic Number 264
17.6 Achromatic Number 264
17.7 Subchromatic Number 265
17.8 Multiplicative Graphs 265
17.9 Reducible Graph Properties 266
17.10 T Colorings 267
17.11 Game Chromatic Number 268
17.12 Harary and Tuza s Coloring Games 269
17.13 Coloring Extension Game 270
17.14 Winning Hex 271
Bibliography 272
Author Index 277
Subject Index 287
|
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| language | English |
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| spelling | Jensen, Tommy R. Verfasser aut Graph coloring problems Tommy R. Jensen, Bjarne Toft, Odense University New York, NY [u.a.] Wiley 1995 XIX, 295 Seiten graph. Darst. txt rdacontent n rdamedia nc rdacarrier Wiley Interscience Series in Discrete Mathematics and Optimization A Wiley Interscience Publication Graphentheorie (DE-588)4113782-6 gnd rswk-swf Graphfärbung (DE-588)4472286-2 gnd rswk-swf Graphfärbung (DE-588)4472286-2 s DE-604 Graphentheorie (DE-588)4113782-6 s Toft, Bjarne Verfasser aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006890521&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Jensen, Tommy R. Toft, Bjarne Graph coloring problems Graphentheorie (DE-588)4113782-6 gnd Graphfärbung (DE-588)4472286-2 gnd |
| subject_GND | (DE-588)4113782-6 (DE-588)4472286-2 |
| title | Graph coloring problems |
| title_auth | Graph coloring problems |
| title_exact_search | Graph coloring problems |
| title_full | Graph coloring problems Tommy R. Jensen, Bjarne Toft, Odense University |
| title_fullStr | Graph coloring problems Tommy R. Jensen, Bjarne Toft, Odense University |
| title_full_unstemmed | Graph coloring problems Tommy R. Jensen, Bjarne Toft, Odense University |
| title_short | Graph coloring problems |
| title_sort | graph coloring problems |
| topic | Graphentheorie (DE-588)4113782-6 gnd Graphfärbung (DE-588)4472286-2 gnd |
| topic_facet | Graphentheorie Graphfärbung |
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