Product graphs: structure and recognition
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York [u.a.]
Wiley
2000
|
| Series: | Wiley-Interscience series in discrete mathematics and optimization
A Wiley-Interscience publication |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XV, 358 S. graph. Darst. |
| ISBN: | 0471370398 |
Staff View
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Record in the Search Index
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| adam_text | Contents
Foreword xi
Preface xiii
Introduction 1
1 Basic concepts 5
1.1 Graphs 5
1.2 Automorphisms and invariants 14
1.3 Hypercubes and isometric subgraphs 19
1.4 The Cartesian product 27
1.5 Graph representations and algorithms 33
1.6 Exercises 44
2 Hypercubes 47
2.1 The Djokovic Winkler relation 6 47
2.2 An application to chemical graphs 58
2.3 Mulder s convex expansion 64
2.4 Retracts and fixed cubes 73
2.5 Notes 79
2.6 Exercises 81
3 Hamming graphs 84
3.1 Canonical isometric embeddings 84
3.2 A dynamic location problem 91
3.3 Quasi median graphs 95
3.4 Recognition algorithms 103
3.5 Notes Ill
3.6 Exercises 113
4 Cartesian products 115
4.1 Prime factor decompositions 116
4.2 Automorphisms 125
4.3 Fixed box theorems 133
4.4 Notes 143
4.5 Exercises 145
vii
viii CONTENTS
5 Strong and direct products 147
5.1 Strong products and retracts 148
5.2 Factoring strong products 153
5.3 Direct products in F and Fo 162
5.4 Factoring direct products 167
5.5 Recognition of direct and strong products 178
5.6 Notes 181
5.7 Exercises 182
6 Lexicographic products 184
6.1 Basic algebraic properties 184
6.2 Factorizations and nonuniqueness 193
6.3 Automorphisms 196
6.4 Recognition complexity 200
6.5 Notes 204
6.6 Exercises 205
7 Fast recognition algorithms 207
7.1 Arboricity, squares, and triangles 207
7.2 Fast recognition of median graphs 217
7.3 Triangle free graphs and median graphs 226
7.4 Fast recognition of Cartesian products 233
7.5 Notes 242
7.6 Exercises 243
8 Invariants 244
8.1 Invariants and standard products 244
8.2 Hedetniemi s conjecture 252
8.3 Coloring lexicographic products 261
8.4 Fractional and circular chromatic number 267
8.5 Shannon capacity 274
8.6 Vizing s conjecture 279
8.7 Notes 287
8.8 Exercises 289
A Selected results and conjectures 291
A.I One factorizations 291
A.2 Hamiltonian decomposable graphs 294
A.3 Perfect graphs 297
A.4 Ultimate independence ratio 300
A.5 Short remarks 301
A.6 Exercises 303
CONTENTS ix
B Infinite graphs 305
B.I Trees, partial cubes, and Hamming graphs 306
B.2 Cartesian products 307
B.3 Strong and direct products 309
B.4 Lexicographic products 311
B.5 Exercises 312
C Other graph products 314
Cl Simple products 314
C.2 Associative simple products 317
C.3 The modular product 321
C.4 Graph exponentiation 322
C5 Exercises 323
Bibliography 324
Name Index 345
Subject Index 349
Symbol Index 357
|
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| illustrated | Illustrated |
| indexdate | 2024-07-09T18:38:13Z |
| institution | BVB |
| isbn | 0471370398 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-008889005 |
| oclc_num | 247799938 |
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| physical | XV, 358 S. graph. Darst. |
| publishDate | 2000 |
| publishDateSearch | 2000 |
| publishDateSort | 2000 |
| publisher | Wiley |
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| series2 | Wiley-Interscience series in discrete mathematics and optimization A Wiley-Interscience publication |
| spelling | Imrich, Wilfried 1941- Verfasser (DE-588)136160832 aut Product graphs structure and recognition Wilfried Imrich ; Sandi Klavžar New York [u.a.] Wiley 2000 XV, 358 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Wiley-Interscience series in discrete mathematics and optimization A Wiley-Interscience publication Graph - Produkt <Mathematik> - Lehrbuch Graph (DE-588)4021842-9 gnd rswk-swf Produkt Mathematik (DE-588)4126359-5 gnd rswk-swf Graph (DE-588)4021842-9 s Produkt Mathematik (DE-588)4126359-5 s DE-604 Klavžar, Sandi 1962- Verfasser (DE-588)171630033 aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008889005&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Imrich, Wilfried 1941- Klavžar, Sandi 1962- Product graphs structure and recognition Graph - Produkt <Mathematik> - Lehrbuch Graph (DE-588)4021842-9 gnd Produkt Mathematik (DE-588)4126359-5 gnd |
| subject_GND | (DE-588)4021842-9 (DE-588)4126359-5 |
| title | Product graphs structure and recognition |
| title_auth | Product graphs structure and recognition |
| title_exact_search | Product graphs structure and recognition |
| title_full | Product graphs structure and recognition Wilfried Imrich ; Sandi Klavžar |
| title_fullStr | Product graphs structure and recognition Wilfried Imrich ; Sandi Klavžar |
| title_full_unstemmed | Product graphs structure and recognition Wilfried Imrich ; Sandi Klavžar |
| title_short | Product graphs |
| title_sort | product graphs structure and recognition |
| title_sub | structure and recognition |
| topic | Graph - Produkt <Mathematik> - Lehrbuch Graph (DE-588)4021842-9 gnd Produkt Mathematik (DE-588)4126359-5 gnd |
| topic_facet | Graph - Produkt <Mathematik> - Lehrbuch Graph Produkt Mathematik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008889005&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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