Integer flows and cycle covers of graphs:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York, NY [u.a.]
Marcel Dekker
1997
|
| Schriftenreihe: | Pure and Applied Mathematics
205 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XII, 379 Seiten graph. Darst. |
| ISBN: | 0824797906 |
Internformat
MARC
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Datensatz im Suchindex
| _version_ | 1804126152934031360 |
|---|---|
| adam_text | Contents
Preface v
I Integer Flows
1 Introduction to Integer Flows 3
1.1 Definitions and Tutte s conjectures 3
1.2 Elementary properties of flows 5
1.3 Modular flows 9
1.4 Flows and face colorings 12
1.5 Exercises 21
2 Basic Properties of Integer Flows 25
2.1 Product of flows 25
2.2 Group flows 27
2.3 Bounded orientations 28
2.4 Cycle covers 30
2.5 Orientable cycle double cover 33
2.6 Sum of flows 35
2.7 Flow polynomial 37
2.8 Minimal counterexamples 38
2.9 Exercises 45
3 Nowhere Zero 4 Flows 49
3.1 Cycle covers and 4 flows 50
3.2 Parity subgraph decompositions 51
3.3 Evenly spanning cycles 53
3.4 4 edge connected graphs 58
ix
x CONTENTS
3.5 Faithful cycle covers 59
3.G Orientable cycle double covers 62
3.7 Snarks 63
3.8 Collapsible graphs 76
3.9 Beyond the 4 color theorem 81
3.10 Exercises 84
3.11 Open problems 90
4 Nowhere Zero 3 Flows 93
4.1 Modular 3 orientations 93
4.2 Orientable cycle double covers 95
4.3 Weak 3 flow conjecture 96
4.4 3 color theorems 98
4.5 Exercises 106
4.6 Open problems 107
5 Nowhere Zero A; Flows (A; 5) 109
5.1 5 color theorem 110
5.2 8 flow theorem 112
5.3 6 flow theorem 114
5.4 Structure of 6 flow 117
5.5 Exercises 119
5.6 Open problems 121
II Cycle Covers
6 Faithful Cycle Covers 125
6.1 Introduction 125
6.2 Minimal contra pairs 127
6.3 Circuit chain 128
6.4 Petersen graph and faithful covers (I) 132
6.5 Petersen graph and faithful covers (II) 133
6.6 Admissible dipath 137
6.7 Planar graphs and faithful covers 140
6.8 Fractional faithful cover 144
6.9 Exercises 146
6.10 Open problems 150
CONTENTS 3d
7 Cycle Double Covers 153
7.1 Double covers and graph embeddings 153
7.2 Minimal counterexamples 155
7.3 Cycle 2k covers 159
7.4 Five cycle double covers 162
7.5 Small circuit double covers 168
7.6 Exercises 169
7.7 Open problems 171
8 Shortest Cycle Covers 175
8.1 Postman tour and shortest cover 175
8.2 Shortest cover and 4 flow (I) 180
8.3 Shortest cover and 4 flow (II) 183
8.4 Shortest cover and 8 flow (I) 184
8.5 Shortest cover and 8 flow (II) 188
8.6 Shortest cover and 6 flow 190
8.7 Shortest cover and 5 flow 197
8.8 Shortest cover and double cover 200
8.9 NP completeness 204
8.10 Exercises 208
8.11 Open problems 210
III Related Topics
9 Generalization and Unification 215
9.1 Circular double covers 215
9.2 Modular orientation 216
9.3 Fractional flows 220
9.4 Cycle space minors 221
9.5 Group connectivity 223
9.6 Exercises 228
9.7 Open problems 231
xii CONTENTS
10 Compatible Decompositions 233
10.1 Introduction 233
10.2 Minimal contra pairs 237
10.3 Planar graphs 242
10.4 Ifs free graphs 243
10.5 Forbidden system reduction 248
10.6 Exercises 258
10.7 Open problems 261
11 Related Topics 263
11.1 Unique edge 3 coloring 263
11.2 Depth of circuit cover 268
11.3 Removable circuits 270
11.4 Even circuit decomposition 275
11.5 Exercises 276
11.6 Open problems 279
IV Appendices
A Fundamental Theorems 283
A.I Some basic theorems 283
A.2 Edge disjoint spanning trees 286
A.3 Cover by perfect matchings 290
A.4 Excluding Petersen minor 293
A.5 Vertex splitting 296
A.6 Exercises 299
A.7 Open problems 300
B Hints for Exercises 303
C Notations and Terminology 337
Bibliography 353
Index 373
|
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| illustrated | Illustrated |
| indexdate | 2024-07-09T18:12:55Z |
| institution | BVB |
| isbn | 0824797906 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007831287 |
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| physical | XII, 379 Seiten graph. Darst. |
| publishDate | 1997 |
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| publishDateSort | 1997 |
| publisher | Marcel Dekker |
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| series | Pure and Applied Mathematics |
| series2 | Pure and Applied Mathematics |
| spelling | Zhang, Cun-Quan Verfasser aut Integer flows and cycle covers of graphs Cun-Quan Zhang New York, NY [u.a.] Marcel Dekker 1997 XII, 379 Seiten graph. Darst. txt rdacontent n rdamedia nc rdacarrier Pure and Applied Mathematics 205 Graphes, Théorie des ram TEORIA DOS GRAFOS larpcal Graph theory Netzwerkfluss (DE-588)4126130-6 gnd rswk-swf Ganzzahlige Lösung (DE-588)4128780-0 gnd rswk-swf Überdeckung Mathematik (DE-588)4186551-0 gnd rswk-swf Kreis Graphentheorie (DE-588)4266835-9 gnd rswk-swf Netzwerkfluss (DE-588)4126130-6 s Ganzzahlige Lösung (DE-588)4128780-0 s DE-604 Kreis Graphentheorie (DE-588)4266835-9 s Überdeckung Mathematik (DE-588)4186551-0 s Pure and Applied Mathematics 205 (DE-604)BV000001885 205 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007831287&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Zhang, Cun-Quan Integer flows and cycle covers of graphs Pure and Applied Mathematics Graphes, Théorie des ram TEORIA DOS GRAFOS larpcal Graph theory Netzwerkfluss (DE-588)4126130-6 gnd Ganzzahlige Lösung (DE-588)4128780-0 gnd Überdeckung Mathematik (DE-588)4186551-0 gnd Kreis Graphentheorie (DE-588)4266835-9 gnd |
| subject_GND | (DE-588)4126130-6 (DE-588)4128780-0 (DE-588)4186551-0 (DE-588)4266835-9 |
| title | Integer flows and cycle covers of graphs |
| title_auth | Integer flows and cycle covers of graphs |
| title_exact_search | Integer flows and cycle covers of graphs |
| title_full | Integer flows and cycle covers of graphs Cun-Quan Zhang |
| title_fullStr | Integer flows and cycle covers of graphs Cun-Quan Zhang |
| title_full_unstemmed | Integer flows and cycle covers of graphs Cun-Quan Zhang |
| title_short | Integer flows and cycle covers of graphs |
| title_sort | integer flows and cycle covers of graphs |
| topic | Graphes, Théorie des ram TEORIA DOS GRAFOS larpcal Graph theory Netzwerkfluss (DE-588)4126130-6 gnd Ganzzahlige Lösung (DE-588)4128780-0 gnd Überdeckung Mathematik (DE-588)4186551-0 gnd Kreis Graphentheorie (DE-588)4266835-9 gnd |
| topic_facet | Graphes, Théorie des TEORIA DOS GRAFOS Graph theory Netzwerkfluss Ganzzahlige Lösung Überdeckung Mathematik Kreis Graphentheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007831287&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000001885 |
| work_keys_str_mv | AT zhangcunquan integerflowsandcyclecoversofgraphs |