Algorithmic graph theory and perfect graphs:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Amsterdam [u.a.]
Elsevier
2004
|
| Edition: | 2. ed. |
| Series: | Annals of discrete mathematics
57 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturangaben 299 - 304 |
| Physical Description: | XXVI, 314 Seiten Diagramme |
| ISBN: | 0444515305 |
Staff View
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| 245 | 1 | 0 | |a Algorithmic graph theory and perfect graphs |c Martin Charles Golumbic |
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Record in the Search Index
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| adam_text | Contents Foreword 2004 xiii Foreword xv Preface xvii Acknowledgments xix List ofSymbols xxi Corrections and Errata CHAPTER 1 Graph Theoretic Foundations 1. 2. 3. 4. CHAPTER 2 xxiii Basic Definitions and Notations Intersection Graphs Interval Graphs—A Sneak Preview of the Notions Coming Up Summary Exercises Bibliography 1 9 13 17 18 20 The Design of Efficient Algorithms 1. 2. 3. 4. The Complexity of Computer Algorithms Data Structures How to Explore a Graph Transitive Tournaments and Topological Sorting Exercises Bibliography 22 31 37 42 45 48 vii
viii chapter Contents 3 Perfect Graphs 1. 2. 3. 4. 5. 6. chapter 4 4. 5. 6. 7. 5 51 53 58 62 65 71 75 77 Triangulated Graphs 1. 2. 3. chapter The Star of the Show The Perfect Graph Theorem p-Critical and Partitionable Graphs A Polyhedral Characterization of Perfect Graphs A Polyhedral Characterization of p-Critical Graphs The Strong Perfect Graph Conjecture Exercises Bibliography Introduction Characterizing Triangulated Graphs Recognizing Triangulated Graphs by Lexicographic Breadth-First Search The Complexity of Recognizing Triangulated Graphs Triangulated Graphs as Intersection Graphs Triangulated Graphs Are Perfect Fast Algorithms for the COLORING, CLIQUE, STABLE SET, and CLIQUE-COVER Problems on Triangulated Graphs Exercises Bibliography 81 81 84 87 91 94 98 100 102 Comparability Graphs 1. 2. 3. 4. 5. 6. 7. Г-Chains and Implication Classes Uniquely Partially Orderable Graphs The Number of Transitive Orientations Schemes and G-Decompositions—An Algorithm for Assigning Transitive Orientations The r*-Matroid of a Graph The Complexity of Comparability Graph Recognition Coloring and Other Problems on Comparability Graphs 105 109 113 120 124 129 132
Contents ¡X 8. CHAPTER 6 2. 3. 7 8 9 149 149 152 155 156 Introduction Characterizing Permutation Graphs Permutation Labelings Applications Sorting a Permutation Using Queues in Parallel Exercises Bibliography 157 158 160 162 164 168 169 Interval Graphs 1. 2. 3. 4. 5. 6. chapter An Introduction to Chapters 6-8: Interval, Permutation, and Split Graphs Characterizing Split Graphs Degree Sequences and Split Graphs Exercises Bibliography Permutation Graphs 1. 2. 3. 4. 5. chapter 135 139 142 Split Graphs 1. chapter The Dimension of Partial Orders Exercises Bibliography How It All Started Some Characterizations of Interval Graphs The Complexity of Consecutive l’s Testing Applications of Interval Graphs Preference and Indifference Circular-Arc Graphs Exercises Bibliography 171 172 175 181 185 188 193 197 Superperfect Graphs 1. 2. 3. Coloring Weighted Graphs Superperfection An Infinite Class of Superperfect Noncomparability Graphs 203 206 209
x Contents 4. 5. 6. chapter 10 11 2. 3. 4. 5. 12 215 218 218 The Threshold Dimension Degree Partition of Threshold Graphs A Characterization Using Permutations An Application to Synchronizing Parallel Processes Exercises Bibliography 219 223 227 229 231 234 Not So Perfect Graphs 1. chapter 212 214 Threshold Graphs 1. 2. 3. 4. chapter When Does Superperfect EqualComparability? Composition of Superperfect Graphs A Representation Using the Consecutive 1 ’s Property Exercises Bibliography Sorting a Permutation Using Stacks in Parallel Intersecting Chords of a Circle Overlap Graphs Fast Algorithms for Maximum Stable Set and Maximum Clique of These Not So Perfect Graphs A Graph Theoretic Characterization of Overlap Graphs Exercises Bibliography 235 237 242 244 248 251 253 Perfect Gaussian Elimination 1. Perfect Elimination Matrices 2. Symmetric Matrices 3. Perfect Elimination Bipartite Graphs 4. Chordal Bipartite Graphs Exercises Bibliography 254 256 259 261 264 266
xi Contents Appendix A. B. C. D. E. F. A Small Collection of NP-Complete Problems An Algorithm for Set Union, Intersection, Difference, and Symmetric Difference of 1 vo Subsets Topological Sorting: An Example of Algorithm 2.4 An Illustration of the Decomposition Algorithm The Properties P.E.B., C.B., (P.E.B.) , (C.B.) Illustrated The Properties C, C, T, T Illustrated 269 270 271 273 273 275 Epilogue 2004 277 Index 307
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| adam_txt |
Contents Foreword 2004 xiii Foreword xv Preface xvii Acknowledgments xix List ofSymbols xxi Corrections and Errata CHAPTER 1 Graph Theoretic Foundations 1. 2. 3. 4. CHAPTER 2 xxiii Basic Definitions and Notations Intersection Graphs Interval Graphs—A Sneak Preview of the Notions Coming Up Summary Exercises Bibliography 1 9 13 17 18 20 The Design of Efficient Algorithms 1. 2. 3. 4. The Complexity of Computer Algorithms Data Structures How to Explore a Graph Transitive Tournaments and Topological Sorting Exercises Bibliography 22 31 37 42 45 48 vii
viii chapter Contents 3 Perfect Graphs 1. 2. 3. 4. 5. 6. chapter 4 4. 5. 6. 7. 5 51 53 58 62 65 71 75 77 Triangulated Graphs 1. 2. 3. chapter The Star of the Show The Perfect Graph Theorem p-Critical and Partitionable Graphs A Polyhedral Characterization of Perfect Graphs A Polyhedral Characterization of p-Critical Graphs The Strong Perfect Graph Conjecture Exercises Bibliography Introduction Characterizing Triangulated Graphs Recognizing Triangulated Graphs by Lexicographic Breadth-First Search The Complexity of Recognizing Triangulated Graphs Triangulated Graphs as Intersection Graphs Triangulated Graphs Are Perfect Fast Algorithms for the COLORING, CLIQUE, STABLE SET, and CLIQUE-COVER Problems on Triangulated Graphs Exercises Bibliography 81 81 84 87 91 94 98 100 102 Comparability Graphs 1. 2. 3. 4. 5. 6. 7. Г-Chains and Implication Classes Uniquely Partially Orderable Graphs The Number of Transitive Orientations Schemes and G-Decompositions—An Algorithm for Assigning Transitive Orientations The r*-Matroid of a Graph The Complexity of Comparability Graph Recognition Coloring and Other Problems on Comparability Graphs 105 109 113 120 124 129 132
Contents ¡X 8. CHAPTER 6 2. 3. 7 8 9 149 149 152 155 156 Introduction Characterizing Permutation Graphs Permutation Labelings Applications Sorting a Permutation Using Queues in Parallel Exercises Bibliography 157 158 160 162 164 168 169 Interval Graphs 1. 2. 3. 4. 5. 6. chapter An Introduction to Chapters 6-8: Interval, Permutation, and Split Graphs Characterizing Split Graphs Degree Sequences and Split Graphs Exercises Bibliography Permutation Graphs 1. 2. 3. 4. 5. chapter 135 139 142 Split Graphs 1. chapter The Dimension of Partial Orders Exercises Bibliography How It All Started Some Characterizations of Interval Graphs The Complexity of Consecutive l’s Testing Applications of Interval Graphs Preference and Indifference Circular-Arc Graphs Exercises Bibliography 171 172 175 181 185 188 193 197 Superperfect Graphs 1. 2. 3. Coloring Weighted Graphs Superperfection An Infinite Class of Superperfect Noncomparability Graphs 203 206 209
x Contents 4. 5. 6. chapter 10 11 2. 3. 4. 5. 12 215 218 218 The Threshold Dimension Degree Partition of Threshold Graphs A Characterization Using Permutations An Application to Synchronizing Parallel Processes Exercises Bibliography 219 223 227 229 231 234 Not So Perfect Graphs 1. chapter 212 214 Threshold Graphs 1. 2. 3. 4. chapter When Does Superperfect EqualComparability? Composition of Superperfect Graphs A Representation Using the Consecutive 1 ’s Property Exercises Bibliography Sorting a Permutation Using Stacks in Parallel Intersecting Chords of a Circle Overlap Graphs Fast Algorithms for Maximum Stable Set and Maximum Clique of These Not So Perfect Graphs A Graph Theoretic Characterization of Overlap Graphs Exercises Bibliography 235 237 242 244 248 251 253 Perfect Gaussian Elimination 1. Perfect Elimination Matrices 2. Symmetric Matrices 3. Perfect Elimination Bipartite Graphs 4. Chordal Bipartite Graphs Exercises Bibliography 254 256 259 261 264 266
xi Contents Appendix A. B. C. D. E. F. A Small Collection of NP-Complete Problems An Algorithm for Set Union, Intersection, Difference, and Symmetric Difference of 1\vo Subsets Topological Sorting: An Example of Algorithm 2.4 An Illustration of the Decomposition Algorithm The Properties P.E.B., C.B., (P.E.B.)', (C.B.)' Illustrated The Properties C, C, T, T Illustrated 269 270 271 273 273 275 Epilogue 2004 277 Index 307 |
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| indexdate | 2024-07-09T20:50:40Z |
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| series | Annals of discrete mathematics |
| series2 | Annals of discrete mathematics |
| spelling | Golumbic, Martin Charles 1948- Verfasser (DE-588)1089493622 aut Algorithmic graph theory and perfect graphs Martin Charles Golumbic 2. ed. Amsterdam [u.a.] Elsevier 2004 XXVI, 314 Seiten Diagramme txt rdacontent n rdamedia nc rdacarrier Annals of discrete mathematics 57 Literaturangaben 299 - 304 Perfect graphs Graph (DE-588)4021842-9 gnd rswk-swf Komplexitätstheorie (DE-588)4120591-1 gnd rswk-swf Graphentheorie (DE-588)4113782-6 gnd rswk-swf Graph (DE-588)4021842-9 s DE-604 Graphentheorie (DE-588)4113782-6 s Komplexitätstheorie (DE-588)4120591-1 s Annals of discrete mathematics 57 (DE-604)BV004511910 57 Digitalisierung UB Passau - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015317969&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Golumbic, Martin Charles 1948- Algorithmic graph theory and perfect graphs Annals of discrete mathematics Perfect graphs Graph (DE-588)4021842-9 gnd Komplexitätstheorie (DE-588)4120591-1 gnd Graphentheorie (DE-588)4113782-6 gnd |
| subject_GND | (DE-588)4021842-9 (DE-588)4120591-1 (DE-588)4113782-6 |
| title | Algorithmic graph theory and perfect graphs |
| title_auth | Algorithmic graph theory and perfect graphs |
| title_exact_search | Algorithmic graph theory and perfect graphs |
| title_exact_search_txtP | Algorithmic graph theory and perfect graphs |
| title_full | Algorithmic graph theory and perfect graphs Martin Charles Golumbic |
| title_fullStr | Algorithmic graph theory and perfect graphs Martin Charles Golumbic |
| title_full_unstemmed | Algorithmic graph theory and perfect graphs Martin Charles Golumbic |
| title_short | Algorithmic graph theory and perfect graphs |
| title_sort | algorithmic graph theory and perfect graphs |
| topic | Perfect graphs Graph (DE-588)4021842-9 gnd Komplexitätstheorie (DE-588)4120591-1 gnd Graphentheorie (DE-588)4113782-6 gnd |
| topic_facet | Perfect graphs Graph Komplexitätstheorie Graphentheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015317969&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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