The game of cops and robbers on graphs:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Providence, Rhode Island
American Mathematical Society
[2011]
|
| Schriftenreihe: | Student mathematical library
volume 61 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | xix, 276 Seiten Illustrationen, Diagramme |
| ISBN: | 9780821853474 |
Internformat
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Datensatz im Suchindex
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| adam_text |
Titel: The game of cops and robbers on graphs
Autor: Bonato, Anthony
Jahr: 2011
Contents
List of Figures xi
Preface xv
Chapter 1. Introduction 1
§1.1. The Game 1
§1.2. Interlude on Notation 5
§1.3. Lower Bounds 10
§1.4. Upper Bounds 16
§1.5. Cops, Robbers, and Retracts 20
Exercises 23
Chapter 2. Characterizations 29
§2.1. Introduction 29
§2.2. Characterizing Cop-win Graphs 30
§2.3. Characterizing Graphs with Higher Cop Number 39
Exercises 48
Chapter 3. Meyniel's Conjecture 53
§3.1. Introduction 53
§3.2. An Improved Upper Bound for the Cop Number 56
§3.3. How Close to y/ñ? 62
viii Contents
§3.4. Meyniel's Conjecture in Graph Classes 66
Exercises 73
Chapter 4. Graph Products and Classes 79
§4.1. Introduction 79
§4.2. Cop Numbers and Corners in Products 83
§4.3. Covering by Cop-win Graphs 86
§4.4. Genus of a Graph 92
§4.5. Outerplanar Graphs 95
§4.6. Planar Graphs 98
Exercises 105
Chapter 5. Algorithms 109
§5.1. Introduction 109
§5.2. Background on Complexity 112
§5.3. Polynomial Time with k Fixed 119
§5.4. NP-hard with k Not Fixed 124
§5.5. Open Problems 127
Exercises 128
Chapter 6. Random Graphs 133
§6.1. Introduction 133
§6.2. Constant p and log n Many Cops 136
§6.3. Variable p and Bounds 139
§6.4. The Zig-Zag Theorem 149
§6.5. Cops and Robbers in the Web Graph 153
Exercises 162
Chapter 7. Infinite Graphs 165
§7.1. Introduction 165
§7.2. Introducing the Infinite Random Graph 167
§7.3. Cop Density 172
87.4 Tnfinitp CVinrHal firanhs 178
Contents ix
§7.5. Vertex-transitive Cop-win Graphs 182
Exercises 187
Chapter 8. Variants of Cops and Robbers 191
§8.1. Imperfect Information 192
§8.2. Itaps 199
§8.3. Tandem-win 203
§8.4. Playing on Different Edge Sets 205
§8.5. Distance k Cops and Robbers 209
§8.6. Capture Time 215
Exercises 219
Chapter 9. Good Guys Versus Bad Guys 221
§9.1. Introduction 221
§9.2. Firefighter 223
§9.3. Seepage 230
§9.4. Graph Searching 233
§9.5. Helicopter Cops and Robbers and Marshals 237
§9.6. Cleaning 239
§9.7. Combinatorial Games 252
Exercises 256
Bibliography 259
Index 273 |
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| indexdate | 2024-11-27T11:04:24Z |
| institution | BVB |
| isbn | 9780821853474 |
| language | English |
| lccn | 2011014177 |
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| spelling | Bonato, Anthony 1971- Verfasser (DE-588)1029584354 aut The game of cops and robbers on graphs Anthony Bonato ; Richard J. Nowakowski Providence, Rhode Island American Mathematical Society [2011] © 2011 xix, 276 Seiten Illustrationen, Diagramme txt rdacontent n rdamedia nc rdacarrier Student mathematical library volume 61 Graphentheorie (DE-588)4113782-6 gnd rswk-swf Algorithmische Spieltheorie (DE-588)1133091814 gnd rswk-swf Vertex-Modell (DE-588)4337907-2 gnd rswk-swf Mathematisches Spiel (DE-588)4139588-8 gnd rswk-swf (DE-588)4151278-9 Einführung gnd-content Graphentheorie (DE-588)4113782-6 s DE-604 Mathematisches Spiel (DE-588)4139588-8 s Algorithmische Spieltheorie (DE-588)1133091814 s Vertex-Modell (DE-588)4337907-2 s Nowakowski, Richard J. 1952- Verfasser (DE-588)1029585229 aut Erscheint auch als Online-Ausgabe 978-1-4704-1656-0 Student mathematical library volume 61 (DE-604)BV013184751 61 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024392794&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Bonato, Anthony 1971- Nowakowski, Richard J. 1952- The game of cops and robbers on graphs Student mathematical library Graphentheorie (DE-588)4113782-6 gnd Algorithmische Spieltheorie (DE-588)1133091814 gnd Vertex-Modell (DE-588)4337907-2 gnd Mathematisches Spiel (DE-588)4139588-8 gnd |
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| title | The game of cops and robbers on graphs |
| title_auth | The game of cops and robbers on graphs |
| title_exact_search | The game of cops and robbers on graphs |
| title_full | The game of cops and robbers on graphs Anthony Bonato ; Richard J. Nowakowski |
| title_fullStr | The game of cops and robbers on graphs Anthony Bonato ; Richard J. Nowakowski |
| title_full_unstemmed | The game of cops and robbers on graphs Anthony Bonato ; Richard J. Nowakowski |
| title_short | The game of cops and robbers on graphs |
| title_sort | the game of cops and robbers on graphs |
| topic | Graphentheorie (DE-588)4113782-6 gnd Algorithmische Spieltheorie (DE-588)1133091814 gnd Vertex-Modell (DE-588)4337907-2 gnd Mathematisches Spiel (DE-588)4139588-8 gnd |
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