The four-color theorem: history, topological foundations, and idea of proof
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | German English |
| Veröffentlicht: |
New York, NY [u.a.]
Springer
1998
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| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Literaturverzeichnis Seiten 231 - 247 |
| Beschreibung: | XVI, 260 Seiten Ill., graph. Darst. |
| ISBN: | 0387984976 |
Internformat
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| 245 | 1 | 0 | |a The four-color theorem |b history, topological foundations, and idea of proof |c Rudolf Fritsch, Gerda Fritsch |
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Datensatz im Suchindex
| _version_ | 1804126814122016768 |
|---|---|
| adam_text | RUDOLF FRITSCH GERDA FRITSCH THE FOUR-COLOR THEOREM HISTORY, TBPOLOGICAL
FOUNDATIONS, AND IDEA OF PROOF TRANSLATED BY JULIE PESCHKE WITH 42
ILLUSTRATIONS SPRINGER CONTENTS PREFACE VII ACKNOWLEDGMENTS FOR THE
ENGLISH EDITION XI WAYS TO READ THIS BOOK XIII 1 HISTORY 1 2
(TBPOLOGICAL) MAPS 43 2.1 PRELIMINARY CONSIDERATIONS 43 2.2 BORDERLINES
46 2.3 THE FORMAL DEFINITION OF MAPS 59 2.4 BASIC EXAMPLES 68 2.5
NATIONAL BORDERS 73 2.6 COMMON BORDERLINES 77 2.7 THE EXTENSION OF MAPS
81 3 THE FOUR-COLOR THEOREM (TBPOLOGICAL VERSION) 85 3.1 FORMULATION AND
BASIC APPROACH 85 3.2 FIRST STEPS TOWARDS THE PROOF 87 XV XVI CONTENTS 4
TOPOLOGY TO COMBINATORICS 99 4.1 _ COMPLETE (PLANE) GRAPHS 99 4.2 THE
WAGNER AND FARY THEOREM 105 4.3 THE EULER POLYHEDRAL FORMULA 114 4.4
DUALITY 118 4.5 CUBIC MAPS 125 4.6 COUNTING ARGUMENTS 129 4.7 THE
FIVE-COLOR THEOREM 133 4.8 TAIT S REFORMULATION 134 5 THE FOUR-COLOR
THEOREM (COMBINATORIAL VERSION) 139 5.1 VERTEX COLORINGS 139 5.2 PLANAR
GRAPHS 141 5.3 FORMULATION AND FURTHER ADVANCES 149 5.4 RINGS AND
CONFIGURATIONS 152 5.5 AND NOW, TO THE PROOF! 168 6 REDUCIBILITY 171 6.1
KEMPE CHAIN GAMES 171 6.2 THE BIRKHOFF NUMBER AND SOME HISTORY 184 6.3
TYPES OF REDUCIBILITY 186 6.4 THE DIIRRE-HEESCH ALGORITHM 187 6.5 A-,
B-, AND C-REDUCIBILITY 208 7 THE QUEST FOR UNAVOIDABLE SETS 219 - 7.1
OBSTRUCTIONS AND A RULE OF THUMB 219 7.2 DISCHARGING PROCEDURES 223
BIBLIOGRAPHY 231 WORKS OF REFERENCE 249 INDEX 251
|
| any_adam_object | 1 |
| author | Fritsch, Rudolf 1939-2018 Fritsch, Gerda |
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| author_sort | Fritsch, Rudolf 1939-2018 |
| author_variant | r f rf g f gf |
| building | Verbundindex |
| bvnumber | BV012197471 |
| callnumber-first | Q - Science |
| callnumber-label | QA612 |
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| callnumber-sort | QA 3612.19 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 280 SK 170 SK 890 |
| ctrlnum | (OCoLC)245940268 (DE-599)BVBBV012197471 |
| dewey-full | 511.5 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 511 - General principles of mathematics |
| dewey-raw | 511.5 |
| dewey-search | 511.5 |
| dewey-sort | 3511.5 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV012197471 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T18:23:26Z |
| institution | BVB |
| isbn | 0387984976 |
| language | German English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-008264975 |
| oclc_num | 245940268 |
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| physical | XVI, 260 Seiten Ill., graph. Darst. |
| publishDate | 1998 |
| publishDateSearch | 1998 |
| publishDateSort | 1998 |
| publisher | Springer |
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| spelling | Fritsch, Rudolf 1939-2018 Verfasser (DE-588)131425749 aut Vierfarbensatz The four-color theorem history, topological foundations, and idea of proof Rudolf Fritsch, Gerda Fritsch New York, NY [u.a.] Springer 1998 XVI, 260 Seiten Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Literaturverzeichnis Seiten 231 - 247 Four-color problem Vierfarbensatz (DE-588)4127127-0 gnd rswk-swf Vierfarbensatz (DE-588)4127127-0 s DE-604 Fritsch, Gerda Verfasser aut GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008264975&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Fritsch, Rudolf 1939-2018 Fritsch, Gerda The four-color theorem history, topological foundations, and idea of proof Vierfarbensatz Four-color problem Vierfarbensatz (DE-588)4127127-0 gnd |
| subject_GND | (DE-588)4127127-0 |
| title | The four-color theorem history, topological foundations, and idea of proof |
| title_alt | Vierfarbensatz |
| title_auth | The four-color theorem history, topological foundations, and idea of proof |
| title_exact_search | The four-color theorem history, topological foundations, and idea of proof |
| title_full | The four-color theorem history, topological foundations, and idea of proof Rudolf Fritsch, Gerda Fritsch |
| title_fullStr | The four-color theorem history, topological foundations, and idea of proof Rudolf Fritsch, Gerda Fritsch |
| title_full_unstemmed | The four-color theorem history, topological foundations, and idea of proof Rudolf Fritsch, Gerda Fritsch |
| title_short | The four-color theorem |
| title_sort | the four color theorem history topological foundations and idea of proof |
| title_sub | history, topological foundations, and idea of proof |
| topic | Vierfarbensatz Four-color problem Vierfarbensatz (DE-588)4127127-0 gnd |
| topic_facet | Vierfarbensatz Four-color problem |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008264975&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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