Graphs, colourings and the four-colour theorem:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Oxford [u.a.]
Oxford Univ. Press
2002
|
| Ausgabe: | 1. publ. |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | VIII, 141 S. graph. Darst. |
| ISBN: | 0198510624 0198510616 |
Internformat
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Datensatz im Suchindex
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| adam_text | GRAPHS, COLOURINGS AND THE FOUR-COLOUR THEOREM ROBERT A. WILSON THE
UNIVERSITY OF BIRMINGHAM SUB GSTTINGEN 7 217 191 738 2004 A 2040 OXTORD
UNIVERSITY PRESS CONTENTS INTRODUCTION 1.1 1.2 PRELIMINARIES HISTORY OF
THE FOUR-COLOUR PROBLEM BASIC GRAPH THEORY 2.1 2.2 2.3 2.4 SOME
DEFINITIONS MAPS DUALITY EULER CIRCUITS PART I GRAPHS, MAPS AND THE
FOUR-COLOUR PROBLEM 3 4 6 6 11 12 15 3 APPLICATIONS OF EULER S FORMULA
19 3.1 EULER S FORMULA , 19 3.2 APPLICATIONS 23 4 KEMPE S APPROACH 31
4.1 THE FIRST PROOF OF THE FOUR-COLOUR THEOREM 31 4.2 THE FIVE-COLOUR
THEOREM 33 4.3 A REDUCTION THEOREM , 35 4.4 VERTEX-COLOURING OF GRAPHS
37 4.5 A THREE-COLOUR THEOREM 38 PART II RELATED TOPICS 5 OTHER
APPROACHES TO THE FOUR-COLOUR PROBLEM 43 5.1 HAMILTON CYCLES 43 5.2
EDGE-COLOURINGS 48 5.3 MORE ON EDGE-COLOURING 51 6 MAPS ON SURFACES WITH
HOLES 58 6.1 SOME TOPOLOGY 58 6.2 MAP COLOURING ON A TORUS 61 6.3
GENERALIZING TO SURFACES OF HIGHER GENUS 64 6.4 NON-ORIENTABLE SURFACES
68 7 KURATOWSKI S THEOREM 72 7.1 CONNECTIVITY 72 7.2 A MINIMAL
COUNTEREXAMPLE TO KURATOWSKI S THEOREM 76 VII VIII CONTENTS 7.3 THE
PROOF OF KURATOWSKI S THEOREM 77 7.4 AN ALTERNATIVE APPROACH 82 8
COLOURING NON-PLANAR GRAPHS 88 8.1 BROOKS THEOREM 88 8.2 THE CHROMATIC
NUMBER 91 8.3 HADWIGER S CONJECTURE 95 8.4 THE HAJOS CONJECTURE 97 8.5
THE CHROMATIC POLYNOMIAL 99 PART III HOW TO PROVE THE FOUR-COLOUR
THEOREM 9 OVERVIEW 107 9.1 HISTORICAL REMARKS 107 9.2 ELEMENTARY
REDUCTIONS 108 9.3 STRATEGY 109 9.4 LATER IMPROVEMENTS 110 10
REDUCIBILITY 111 10.1 THE BIRKHOFF DIAMOND 111 10.2 REDUCING SMALL
CYCLES 114 10.3 BIRKHOFF S REDUCTION THEOREM 116 10.4 LARGER
CONFIGURATIONS 119 10.5 USING A COMPUTER TO PROVE REDUCIBILITY 121 11
DISCHARGING 125 11.1 UNAVOIDABLE SETS 125 11.2 SIMPLE EXAMPLES OF
DISCHARGING 128 11.3 A MORE COMPLICATED DISCHARGING ALGORITHM 130 11.4
CONCLUSION 132 BIBLIOGRAPHY 136 INDEX 139
|
| any_adam_object | 1 |
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| discipline | Mathematik |
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| illustrated | Illustrated |
| indexdate | 2024-07-09T19:04:59Z |
| institution | BVB |
| isbn | 0198510624 0198510616 |
| language | English |
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| physical | VIII, 141 S. graph. Darst. |
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| spelling | Wilson, Robert A. Verfasser aut Graphs, colourings and the four-colour theorem Robert A. Wilson 1. publ. Oxford [u.a.] Oxford Univ. Press 2002 VIII, 141 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Grafentheorie gtt Problème des quatre couleurs Vierkleurenprobleem gtt Four-color problem Graph coloring Vierfarbensatz (DE-588)4127127-0 gnd rswk-swf Färben (DE-588)4016254-0 gnd rswk-swf Mathematik (DE-588)4037944-9 gnd rswk-swf Graph (DE-588)4021842-9 gnd rswk-swf Graph (DE-588)4021842-9 s Färben (DE-588)4016254-0 s Mathematik (DE-588)4037944-9 s Vierfarbensatz (DE-588)4127127-0 s DE-604 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009957770&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Wilson, Robert A. Graphs, colourings and the four-colour theorem Grafentheorie gtt Problème des quatre couleurs Vierkleurenprobleem gtt Four-color problem Graph coloring Vierfarbensatz (DE-588)4127127-0 gnd Färben (DE-588)4016254-0 gnd Mathematik (DE-588)4037944-9 gnd Graph (DE-588)4021842-9 gnd |
| subject_GND | (DE-588)4127127-0 (DE-588)4016254-0 (DE-588)4037944-9 (DE-588)4021842-9 |
| title | Graphs, colourings and the four-colour theorem |
| title_auth | Graphs, colourings and the four-colour theorem |
| title_exact_search | Graphs, colourings and the four-colour theorem |
| title_full | Graphs, colourings and the four-colour theorem Robert A. Wilson |
| title_fullStr | Graphs, colourings and the four-colour theorem Robert A. Wilson |
| title_full_unstemmed | Graphs, colourings and the four-colour theorem Robert A. Wilson |
| title_short | Graphs, colourings and the four-colour theorem |
| title_sort | graphs colourings and the four colour theorem |
| topic | Grafentheorie gtt Problème des quatre couleurs Vierkleurenprobleem gtt Four-color problem Graph coloring Vierfarbensatz (DE-588)4127127-0 gnd Färben (DE-588)4016254-0 gnd Mathematik (DE-588)4037944-9 gnd Graph (DE-588)4021842-9 gnd |
| topic_facet | Grafentheorie Problème des quatre couleurs Vierkleurenprobleem Four-color problem Graph coloring Vierfarbensatz Färben Mathematik Graph |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009957770&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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