The four-color problem:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York [u.a.]
Acad. Pr.
1968
|
| Edition: | 2. print. |
| Series: | Pure and applied mathematics
27 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XV, 259 S. Ill. |
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MARC
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Record in the Search Index
| _version_ | 1804123405920763904 |
|---|---|
| adam_text | CONTENTS
Preface vii
Introduction xi
Chapter 1 / Planar Graphs
I. I. Planar Representations I
1.2. The Faces 2
1.3. Maximal Planar Graphs. Straight Line Representations 5
Chapter 2 / Bridges and Circuits
2.1. Bridges in General Graphs 12
2.2. Circuit Bridges 13
2.3. Equivalence of Planar Representations 16
2.4. Uniqueness of Representations 18
2.5. Transfer of Bridges 19
2.6. Characterization of Planar Graphs 21
2.7. Further Observations on Maximal Graphs 25
Chapter 3 / Dual Graphs
3.1. Geometric Definition of Duality 30
3.2. Observations on Graphs and Their Duals 33
3.3. Relational Definition of Duality 36
3.4. Characterization of Planar Graphs 41
3.5. Maximal Bipartite Graphs. Self Dual Graphs 44
Chapter 4 / Euler s Formula and Its Consequences
4.1. Euler s Formula 48
4.2. Regular Graphs 52
4.3. The Euler Contributions 54
xiii
xiv Contents
Chapter 5 / Large Circuits
5.1. Circuit Arcs 62
5.2. Hamilton Circuits 68
Chapter 6 / Colorations
6.1. Types of Coloration 75
6.2. Two Colors 77
6.3. Reductions 78
6.4. The Five Color Theorem 84
6.5. The Theorem of Brooks 87
Chapter 7 / Color Functions
7.1. Vertex Coloration 90
7.2. The Dual Theory 92
7.3. Color Directed Graphs 94
7.4. Some Special Applications 98
Chapter 8 / Formulations of the Four Color Problem
8.1. Decomposition into Three Subgraphs 102
8.2. Bipartite Dichotomy 104
8.3. Even Subgraphs 105
8.4. Graphs with Small Face Boundaries 108
8.5. Angle Characters and Congruence Conditions (mod 3) 112
Chapter 9 / Cubic Graphs
9.1. Color Reduction to Cubic Graphs 117
9.2. Configurations in Cubic Graphs 119
9.3. Four Color Conditions in Cubic Graphs 121
9.4. The Interchange Graph and the Color Problems 124
9.5. Planar Interchange Graphs 127
9.6. Construction of Cubic Graphs 129
Chapter 10 / Hadwiger s Conjecture
10.1. Contractions and Subcontractions 134
10.2. Maximal Graphs and Simplex Decompositions 138
10.3. Indecomposable Graphs 143
10.4. Hadwiger s Conjecture 146
10.5. Wagner s Equivalence Theorem 153
10.6. Contractions to S4 158
10.7. Multiply Connected Graphs 160
Contents XV
Chapter 11 / Critical Graphs
11.1. Types of Critical Graphs 164
11.2. Contraction Critical Graphs 167
11.3. Edge Critical Graphs 171
11.4. Construction of c Critical Graphs 175
11.5. Conjunctions and Mergers 180
11.6. Amalgamations 183
11.7. Mergers of Simplexes 186
Chapter 12 / Planar 5 Chromatic Graphs
12.1. Separations 192
12.2. Irreducible Graphs 196
12.3. Reductions for Minor Vertices 198
12.4. Errera Circuits and 5 Components 210
12.5. Lower Bounds for Irreducible Graphs 215
Chapter 13/ Three Colors
13.1. Formulations of the Three Color Problem 226
13.2. The Theorem of Grotzsch 230
Chapter 14 / Edge Coloration
14.1. General Observations 240
14.2. Coloration of an Augmented Graph 242
14.3. The Theorem of Shannon 244
14.4. The Theorem of Vizing 246
Bibliography 249
Author Index 255
Subject Index 257
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| indexdate | 2024-07-09T17:29:15Z |
| institution | BVB |
| language | English |
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| physical | XV, 259 S. Ill. |
| publishDate | 1968 |
| publishDateSearch | 1968 |
| publishDateSort | 1968 |
| publisher | Acad. Pr. |
| record_format | marc |
| series | Pure and applied mathematics |
| series2 | Pure and applied mathematics |
| spelling | Ore, Oystein Verfasser aut The four-color problem Oystein Ore 2. print. New York [u.a.] Acad. Pr. 1968 XV, 259 S. Ill. txt rdacontent n rdamedia nc rdacarrier Pure and applied mathematics 27 Vierfarbensatz Vierfarbensatz (DE-588)4127127-0 gnd rswk-swf Graphentheorie (DE-588)4113782-6 gnd rswk-swf Vierfarbensatz (DE-588)4127127-0 s DE-604 Graphentheorie (DE-588)4113782-6 s Pure and applied mathematics 27 (DE-604)BV010177228 27 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=005990008&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Ore, Oystein The four-color problem Pure and applied mathematics Vierfarbensatz Vierfarbensatz (DE-588)4127127-0 gnd Graphentheorie (DE-588)4113782-6 gnd |
| subject_GND | (DE-588)4127127-0 (DE-588)4113782-6 |
| title | The four-color problem |
| title_auth | The four-color problem |
| title_exact_search | The four-color problem |
| title_full | The four-color problem Oystein Ore |
| title_fullStr | The four-color problem Oystein Ore |
| title_full_unstemmed | The four-color problem Oystein Ore |
| title_short | The four-color problem |
| title_sort | the four color problem |
| topic | Vierfarbensatz Vierfarbensatz (DE-588)4127127-0 gnd Graphentheorie (DE-588)4113782-6 gnd |
| topic_facet | Vierfarbensatz Graphentheorie |
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