Graphs on surfaces:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Baltimore, Md. [u.a.]
<<The>> Johns Hopkins University Press
2001
|
| Schriftenreihe: | Johns Hopkins Studies in the Mathematical Sciences
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XI, 291 Seiten Illustrationen |
| ISBN: | 0801866898 |
Internformat
MARC
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Datensatz im Suchindex
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|---|---|
| adam_text | IMAGE 1
GRAPHS ON SURFACES
BOJAN MOHAER AND
CARSTEN THOMASSEN
THE JOHNS HOPKINS UNIVERSITY PRESS
BALTIMORE AND LONDON
IMAGE 2
CONTENTS
PREFACE IX
CHAPTER 1. 1.1. 1.2. 1.3.
1.4.
CHAPTER 2. 2.1. 2.2. 2.3.
2.4. 2.5. 2.6.
2.7. 2.8. 2.9. 2.10.
CHAPTER 3. 3.1. 3.2. 3.3. 3.4. 3.5.
CHAPTER 4.
4.1. 4.2 4.3
4.4 4.5.
INTRODUCTION BASIC DEFINITIONS TREES AND BIPARTITE GRAPHS BLOCKS
CONNECTIVITY
PLANAR GRAPHS PLANAR GRAPHS AND THE JORDAN CURVE THEOREM THE
JORDAN-SCHOENFLIES THEOREM THE THEOREM OF KURATOWSKI
CHARACTERIZATIONS OF PLANAR GRAPHS 3-CONNECTED PLANAR GRAPHS DUAL GRAPHS
PLANARITY ALGORITHMS CIRCLE PACKING REPRESENTATIONS
THE RIEMANN MAPPING THEOREM THE JORDAN CURVE THEOREM AND KURATOWSKI S
THEOREM IN GENERAL TOPOLOGICAL SPACES
SURFACES CLASSIFICATION OF SURFACES ROTATION SYSTEMS EMBEDDING SCHEMES
THE GENUS OF A GRAPH
CLASSIFICATION OF NONCOMPACT SURFACES
EMBEDDINGS COMBINATORIALLY, CONTRACTIBILITY OF CYCLES, AND THE GENUS
PROBLEM EMBEDDINGS COMBINATORIALLY CYCLES OF EMBEDDED GRAPHS THE 3-PATH
CONDITION THE GENUS OF A GRAPH THE MAXIMUM GENUS OF A GRAPH
3
3
8
10 11
17 18 25 30 33 39 42 49 51 64
66
77 78 87
91 94 95
99 99 103 110
112 122
IMAGE 3
VIII
CONTENTS
CHAPTER 5. THE WIDTH OF EMBEDDINGS 129
5.1. EDGE-WIDTH 129
5.2. 2-FLIPPINGS AND UNIQUENESS OF LEW-EMBEDDINGS 135
5.3. TRIANGULATIONS 139
5.4. MINIMAL TRIANGULATIONS OF A GIVEN EDGE-WIDTH 142
5.5. FACE-WIDTH 146
5.6. MINIMAL EMBEDDINGS OF A GIVEN FACE-WIDTH 154
5.7. EMBEDDINGS OF PLANAR GRAPHS 159
5.8. THE GENUS OF A GRAPH WITH A GIVEN NONORIENTABLE EMBEDDING 163
5.9. FACE-WIDTH AND SURFACE MINORS 165
5.10. FACE-WIDTH AND EMBEDDING FLEXIBILITY 167
5.11. COMBINATORIAL PROPERTIES OF EMBEDDED GRAPHS OF LARGE WIDTH 177
CHAPTER 6. EMBEDDING EXTENSIONS AND OBSTRUCTIONS 183
6.1. FORBIDDEN SUBGRAPHS AND FORBIDDEN MINORS 184
6.2. BRIDGES 185
6.3. OBSTRUCTIONS IN A BRIDGE 189
6.4. 2-RESTRICTED EMBEDDING EXTENSIONS 195
6.5. THE FORBIDDEN SUBGRAPHS FOR THE PROJECTIVE PLANE 197
6.6. THE MINIMAL FORBIDDEN SUBGRAPHS FOR GENERAL SURFACES 202
CHAPTER 7. TREE-WIDTH AND THE EXCLUDED MINOR THEOREM 205 7.1. TREE-WIDTH
AND THE EXCLUDED GRID THEOREM 205
7.2. MINIMAL OBSTRUCTIONS OF BOUNDED TREE-WIDTH 215
7.3. THE EXCLUDED MINOR THEOREM FOR ANY FIXED SURFACE 218
CHAPTER 8. COLORINGS OF GRAPHS ON SURFACES 223
8.1. PLANAR GRAPHS ARE 5-CHOOSABLE 223
8.2. THE FOUR COLOR THEOREM 225
8.3. COLOR CRITICAL GRAPHS AND THE HEAWOOD FORMULA 230
8.4. COLORING IN FEW COLORS 235
8.5. GRAPHS WITHOUT SHORT CYCLES 242
APPENDIX A. THE MINIMAL FORBIDDEN SUBGRAPHS FOR THE PROJECTIVE PLANE 247
APPENDIX B. THE UNAVOIDABLE CONFIGURATIONS IN PLANAR
TRIANGULATIONS 253
BIBLIOGRAPHY 265
INDEX 283
|
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| author | Mohar, Bojan Thomassen, Carsten 1948- |
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| ctrlnum | (OCoLC)247993947 (DE-599)BVBBV013868388 |
| 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 |
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| id | DE-604.BV013868388 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T18:53:27Z |
| institution | BVB |
| isbn | 0801866898 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-009485842 |
| oclc_num | 247993947 |
| open_access_boolean | |
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| owner_facet | DE-739 DE-91G DE-BY-TUM DE-11 DE-188 DE-355 DE-BY-UBR DE-83 DE-20 |
| physical | XI, 291 Seiten Illustrationen |
| publishDate | 2001 |
| publishDateSearch | 2001 |
| publishDateSort | 2001 |
| publisher | <<The>> Johns Hopkins University Press |
| record_format | marc |
| series2 | Johns Hopkins Studies in the Mathematical Sciences |
| spelling | Mohar, Bojan Verfasser (DE-588)171082311 aut Graphs on surfaces Bojan Mohar and Carsten Thomassen Baltimore, Md. [u.a.] <<The>> Johns Hopkins University Press 2001 XI, 291 Seiten Illustrationen txt rdacontent n rdamedia nc rdacarrier Johns Hopkins Studies in the Mathematical Sciences Graph - Oberfläche Graph (DE-588)4021842-9 gnd rswk-swf Oberfläche (DE-588)4042907-6 gnd rswk-swf Graph (DE-588)4021842-9 s Oberfläche (DE-588)4042907-6 s DE-604 Thomassen, Carsten 1948- Verfasser (DE-588)1146343620 aut GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009485842&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Mohar, Bojan Thomassen, Carsten 1948- Graphs on surfaces Graph - Oberfläche Graph (DE-588)4021842-9 gnd Oberfläche (DE-588)4042907-6 gnd |
| subject_GND | (DE-588)4021842-9 (DE-588)4042907-6 |
| title | Graphs on surfaces |
| title_auth | Graphs on surfaces |
| title_exact_search | Graphs on surfaces |
| title_full | Graphs on surfaces Bojan Mohar and Carsten Thomassen |
| title_fullStr | Graphs on surfaces Bojan Mohar and Carsten Thomassen |
| title_full_unstemmed | Graphs on surfaces Bojan Mohar and Carsten Thomassen |
| title_short | Graphs on surfaces |
| title_sort | graphs on surfaces |
| topic | Graph - Oberfläche Graph (DE-588)4021842-9 gnd Oberfläche (DE-588)4042907-6 gnd |
| topic_facet | Graph - Oberfläche Graph Oberfläche |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009485842&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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