The Petersen graph:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Cambridge
Cambridge University Press
1993
|
| Edition: | 1. publication |
| Series: | Australian Mathematical Society: Australian Mathematical Society Lecture Series
7 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | 353 Seiten graph. Darst. |
| ISBN: | 0521435943 |
Staff View
MARC
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| 245 | 1 | 0 | |a The Petersen graph |c D. A. Holton, Department of Mathematics and Statistics, University of Otago, New Zealand, J. Sheehan, Department of Mathematical Sciences, University of Aberdeen |
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Record in the Search Index
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|---|---|
| adam_text | Contents
Preface
1 The Petersen graph 1
0. Prologue 1
1. What is a graph? 1
2. Regular graphs and connectivity 11
3. Bipartite graphs 18
4. Automorphism groups 22
5. Hamiltonian graphs 29
6. Planar graphs 33
7. Graph colourings 41
Exercises 42
References 45
2 The Four Colour Problem 49
0. Prologue 49
1. The Five Colour Theorem 50
2. Unavoidable Configurations 56
3. Reducible Configurations 62
4. The Four Colour Theorem 65
5. Hadwiger and Hajos 67
6. Tail s Method 70
Exercises 73
References 76
3 Snarks 79
0. Prologue 79
1. Vizing s Theorem 79
2. Isaacs Snarks 88
3. k snarks (k 3) 102
Exercises 107
References 109
Contents
4 Factors 112
0. Prologue 112
1. Tait s conjecture 113
2. Tutte s characterization 115
3. Petersen s graph 124
4. Factor covered 127
5. f factors 130
6. Applications 139
Exercises 148
References 150
5 Beyond the Four Colour theorem 154
0. Prologue 154
1. Flows 154
2. A Result of Seymour 160
3. Protective Geometry 163
4. Colourings and Projective Spaces 172
5. Epilogue 175
Exercises 176
References 180
6 Cages 183
0. Prologue I83
1. Cages 183
2. Upper Bounds for f(r,g) 190
3. Small Cages 194
4. Symmetry and cages 202
Exercises 209
References 210
7 Hypohamiltonian graphs 214
0. Prologue 214
1. Sousselier s problem 214
2. Petersen generalizations 216
3. A graph for all vertices 222
4. Questions alive and dead 229
5. A nine point theorem 238
Exercises 244
References 246
Contents
8 Symmetry 249
0. Prologue 249
1. Distance transitive graphs 250
2. Distance transitive line graphs 261
3. Rank 3 graphs 262
4. Strongly regular graphs 265
5. Homogeneous graphs 272
Exercises 273
References 275
9 The Petersen Graph in Diversity 279
0. Prologue 279
1. The dodecahedron and P 279
2. Locally Petersen graphs 280
3. Spectral properties of P 282
4. Orientations 286
5. Hamiltonian paths and the Petersen graph 289
6. Kneser s conjecture 295
7. Odd Graphs 297
8. The Johnson graphs and even graphs 300
9. Embeddings 301
10. The cycle double cover conjecture 305
ll.Geodetics 309
12. Geodetics and an extremal problem 313
13. Generalized Petersen and permutation graphs 315
14. Generalized Petersen edge colourings and groups 317
15.Pandora s Box 318
Exercises 321
References 327
Conjecture Index 340
Notation Index 343
Index 345
|
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| id | DE-604.BV007753884 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T17:08:54Z |
| institution | BVB |
| isbn | 0521435943 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-005096783 |
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| physical | 353 Seiten graph. Darst. |
| publishDate | 1993 |
| publishDateSearch | 1993 |
| publishDateSort | 1993 |
| publisher | Cambridge University Press |
| record_format | marc |
| series | Australian Mathematical Society: Australian Mathematical Society Lecture Series |
| series2 | Australian Mathematical Society: Australian Mathematical Society Lecture Series |
| spelling | Holton, Derek Allan 1941- Verfasser (DE-588)115636390 aut The Petersen graph D. A. Holton, Department of Mathematics and Statistics, University of Otago, New Zealand, J. Sheehan, Department of Mathematical Sciences, University of Aberdeen 1. publication Cambridge Cambridge University Press 1993 353 Seiten graph. Darst. txt rdacontent n rdamedia nc rdacarrier Australian Mathematical Society: Australian Mathematical Society Lecture Series 7 kombinatorika - teorija grafov Petersen-Graph (DE-588)4342679-7 gnd rswk-swf Graphentheorie (DE-588)4113782-6 gnd rswk-swf Graphentheorie (DE-588)4113782-6 s DE-604 Petersen-Graph (DE-588)4342679-7 s Sheehan, J. Verfasser aut Australian Mathematical Society: Australian Mathematical Society Lecture Series 7 (DE-604)BV001902595 7 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=005096783&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Holton, Derek Allan 1941- Sheehan, J. The Petersen graph Australian Mathematical Society: Australian Mathematical Society Lecture Series kombinatorika - teorija grafov Petersen-Graph (DE-588)4342679-7 gnd Graphentheorie (DE-588)4113782-6 gnd |
| subject_GND | (DE-588)4342679-7 (DE-588)4113782-6 |
| title | The Petersen graph |
| title_auth | The Petersen graph |
| title_exact_search | The Petersen graph |
| title_full | The Petersen graph D. A. Holton, Department of Mathematics and Statistics, University of Otago, New Zealand, J. Sheehan, Department of Mathematical Sciences, University of Aberdeen |
| title_fullStr | The Petersen graph D. A. Holton, Department of Mathematics and Statistics, University of Otago, New Zealand, J. Sheehan, Department of Mathematical Sciences, University of Aberdeen |
| title_full_unstemmed | The Petersen graph D. A. Holton, Department of Mathematics and Statistics, University of Otago, New Zealand, J. Sheehan, Department of Mathematical Sciences, University of Aberdeen |
| title_short | The Petersen graph |
| title_sort | the petersen graph |
| topic | kombinatorika - teorija grafov Petersen-Graph (DE-588)4342679-7 gnd Graphentheorie (DE-588)4113782-6 gnd |
| topic_facet | kombinatorika - teorija grafov Petersen-Graph Graphentheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=005096783&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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