Coloring mixed hypergraphs: theory, algorithms, and applications
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Providence, Rhode Island
American Mathematical Society
[2002]
|
| Series: | Fields Institute Monographs
17 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturverzeichnis Seiten 171 - 178 |
| Physical Description: | xiii, 181 Seiten Illustrationen, Diagramme |
| ISBN: | 0821828126 9780821828120 |
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| 245 | 1 | 0 | |a Coloring mixed hypergraphs |b theory, algorithms, and applications |c Vitaly I. Voloshin |
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Contents
Preface xiii
Introduction 1
0.1. Overview of graph coloring 1
0.2. Mixed hypergraphs and their coloring 3
0.3. Unforeseen features of mixed hypergraph coloring 3
0.4. Philosophical motivation of mixed hypergraph coloring 4
0.5. Organization 5
0.6. Acknowledgments 9
Chapter 1. The Lower Chromatic Number of a Hypergraph 11
1.1. General concepts 11
1.2. A brief history of coloring theory 16
1.3. Basic results on hypergraph coloring 19
1.4. Hypertrees and chordal conformal hypergraphs 23
Chapter 2. Mixed Hypergraphs and the Upper Chromatic
Number 27
2.1. Basic definitions 27
2.2. Splitting-contraction algorithm 30
2.3. Basic properties of the upper chromatic number 34
2.4. Greedy C-hypergraph coloring algorithms 37
2.5. Algorithmic complexity 42
2.6. Open problems 43
Chapter 3. Uncolorable Mixed Hypergraphs 45
3.1. Minimal uncolorable mixed hypergraphs 45
3.2. Uncolorability measures and a greedy algorithm 48
3.3. Colorability as an integer programming problem 52
3.4. Special types of uncolorable mixed hypergraphs 54
3.5. Open problems 57
Chapter 4. Uniquely Colorable Mixed Hypergraphs 59
4.1. Preliminary 59
4.2. Embeddings into uc mixed hypergraphs 60
4.3. Separation using uc subhypergraphs 61
4.4. Recursive operations 63
4.5. Algorithmic complexity 67
4.6. UC mixed hypergraphs with x n — 2 67
4.7. Uniquely colorable mixed hypertrees 71
ix
x Contents
4.8. Open problems 76
Chapter 5. C-perfect Mixed Hypergraphs 79
5.1. Basic concepts 79
5.2. Minimal non-C-perfect mixed hypergraphs 81
5.3. C-perfection of mixed hypertrees 84
5.4. Algorithmic aspects of C-perfection 85
5.5. Open problems 86
Chapter 6. Gaps in the Chromatic Spectrum 89
6.1. The smallest mixed hypergraphs with gaps 89
6.2. Feasible sets and a doubling-shifting algorithm 91
6.3. Smaller realization 93
6.4. 0-1 realization 95
6.5. Uniform bihypergraphs may have gaps 96
6.6. Separation on uc preserves continuity 98
6.7. Open problems 99
Chapter 7. Interval Mixed Hypergraphs 101
7.1. Colorings 101
7.2. Linear time algorithm for the upper chromatic number 104
7.3. Chromatic spectrum is continuous 105
7.4. Open problems 106
Chapter 8. Pseudo-chordal Mixed Hypergraphs 107
8.1. Preliminaries 107
8.2. Chromatic polynomial 109
8.3. Consequences and examples 111
8.4. A universal formula for chordal graphs 115
8.5. Open problems 117
Chapter 9. Circular Mixed Hypergraphs 119
9.1. Preliminaries 119
9.2. Unique colorability, n even 121
9.3. Unique colorability, n odd 123
9.4. Colorability and lower chromatic number 125
9.5. Upper chromatic number 125
9.6. Open problems 127
Chapter 10. Planar Mixed Hypergraphs 129
10.1. Classic planar hypergraphs 129
10.2. Coloring bitriangulations 130
10.3. Bounds for the upper chromatic number 135
10.4. Gaps in the chromatic spectrum 137
10.5. Open problems 138
Chapter 11. Coloring Block Designs as Mixed Hypergraphs 141
11.1. Steiner systems 141
11.2. Steiner triple systems 143
11.3. Steiner quadruple systems 149
11.4. Open problems 153
Contents xi
Chapter 12. Modelling with Mixed Hypergraphs 155
12.1. List colorings without lists 155
12.2. Ramsey, anti-Ramsey and related problems 156
12.3. Mixed hypergraphs and integer programming 158
12.4. Resource allocation 162
12.5. Lifetime of set systems 165
12.6. Parallel computing 165
12.7. Database management 165
12.8. Molecular biology 166
12.9. Genetics of populations 168
12.10. Natural number interpretation 169
Bibliography 171
List of Figures 179
Index 181 |
| any_adam_object | 1 |
| author | Voloshin, Vitaly I. 1954- |
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| dewey-ones | 511 - General principles of mathematics |
| dewey-raw | 511.5 |
| dewey-search | 511.5 |
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
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| isbn | 0821828126 9780821828120 |
| language | English |
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| physical | xiii, 181 Seiten Illustrationen, Diagramme |
| publishDate | 2002 |
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| spelling | Voloshin, Vitaly I. 1954- Verfasser (DE-588)139301046 aut Coloring mixed hypergraphs theory, algorithms, and applications Vitaly I. Voloshin Providence, Rhode Island American Mathematical Society [2002] © 2002 xiii, 181 Seiten Illustrationen, Diagramme txt rdacontent n rdamedia nc rdacarrier Fields Institute Monographs 17 Literaturverzeichnis Seiten 171 - 178 Hypergraphs Map-coloring problem Hypergraph (DE-588)4161063-5 gnd rswk-swf Graphfärbung (DE-588)4472286-2 gnd rswk-swf Hypergraph (DE-588)4161063-5 s Graphfärbung (DE-588)4472286-2 s DE-604 Erscheint auch als Online-Ausgabe 978-1-4704-3144-0 Fields Institute for Research in Mathematical Sciences <Canada> Fields Institute monographs 17 (DE-604)BV009737926 17 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=022457794&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Voloshin, Vitaly I. 1954- Coloring mixed hypergraphs theory, algorithms, and applications Hypergraphs Map-coloring problem Hypergraph (DE-588)4161063-5 gnd Graphfärbung (DE-588)4472286-2 gnd |
| subject_GND | (DE-588)4161063-5 (DE-588)4472286-2 |
| title | Coloring mixed hypergraphs theory, algorithms, and applications |
| title_auth | Coloring mixed hypergraphs theory, algorithms, and applications |
| title_exact_search | Coloring mixed hypergraphs theory, algorithms, and applications |
| title_full | Coloring mixed hypergraphs theory, algorithms, and applications Vitaly I. Voloshin |
| title_fullStr | Coloring mixed hypergraphs theory, algorithms, and applications Vitaly I. Voloshin |
| title_full_unstemmed | Coloring mixed hypergraphs theory, algorithms, and applications Vitaly I. Voloshin |
| title_short | Coloring mixed hypergraphs |
| title_sort | coloring mixed hypergraphs theory algorithms and applications |
| title_sub | theory, algorithms, and applications |
| topic | Hypergraphs Map-coloring problem Hypergraph (DE-588)4161063-5 gnd Graphfärbung (DE-588)4472286-2 gnd |
| topic_facet | Hypergraphs Map-coloring problem Hypergraph Graphfärbung |
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