Embeddability in graphs:
This monograph provides a theoretical treatment of the problems related to the embeddability of graphs. Among these problems are the planarity and planar embeddings of a graph, the Gaussian crossing problem, the isomorphisms of polyhedra, surface embeddability, problems concerning graphic and cograp...
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Beijing
Science Press [u.a.]
1995
|
| Series: | Mathematics and its application, China series
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Summary: | This monograph provides a theoretical treatment of the problems related to the embeddability of graphs. Among these problems are the planarity and planar embeddings of a graph, the Gaussian crossing problem, the isomorphisms of polyhedra, surface embeddability, problems concerning graphic and cographic matroids and the knot problem from topology to combinatorics are discussed. Rectilinear embeddability, and the net-embeddability of a graph, which appears from the VSLI circuit design and has been much improved by the author recently, is also illustrated. Furthermore, some optimization problems related to planar and rectilinear embeddings of graphs, including those of finding the shortest convex embedding with a boundary condition and the shortest triangulation for given points on the plane, the bend and the area minimizations of rectilinear embeddings, and several kinds of graph decompositions are specially described for conditions efficiently solvable At the end of each chapter, the Notes Section sets out the progress of related problems, the background in theory and practice, and some historical remarks. Some open problems with suggestions for their solutions are mentioned for further research |
| Physical Description: | XVI, 398 S. graph. Darst. |
| ISBN: | 7030047729 |
Staff View
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| 520 | 3 | |a This monograph provides a theoretical treatment of the problems related to the embeddability of graphs. Among these problems are the planarity and planar embeddings of a graph, the Gaussian crossing problem, the isomorphisms of polyhedra, surface embeddability, problems concerning graphic and cographic matroids and the knot problem from topology to combinatorics are discussed. Rectilinear embeddability, and the net-embeddability of a graph, which appears from the VSLI circuit design and has been much improved by the author recently, is also illustrated. Furthermore, some optimization problems related to planar and rectilinear embeddings of graphs, including those of finding the shortest convex embedding with a boundary condition and the shortest triangulation for given points on the plane, the bend and the area minimizations of rectilinear embeddings, and several kinds of graph decompositions are specially described for conditions efficiently solvable | |
| 520 | |a At the end of each chapter, the Notes Section sets out the progress of related problems, the background in theory and practice, and some historical remarks. Some open problems with suggestions for their solutions are mentioned for further research | ||
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Record in the Search Index
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|---|---|
| adam_text | Contents
Preface i
Chapter 1. Preliminaries 1
§1.1 Sets 1
§1.2 Orders 4
§1.3 Graphs 7
§1.4 Groups . 11
§1.5 Surfaces 15
§1.6 Notes 19
Chapter 2. Trees in Graphs 21
§2.1 Trees and cotrees 21
§2.2 OD trees and OD cotrees 26
§2.3 Notes 31
Chapter 3. Spaces in Graphs 33
§3.0 Spaces over GF(2) 33
§3.1 Cycles, cocycles and bicycles 35
§3.2 Cycle spaces 38
§3.3 Cocycle spaces 43
§3.4 Bicycle spaces 49
§3.5 Notes 54
Chapter 4. Planar Graphs 56
§4.1 Usages of the Euler formula 56
xiv Contents
§4.2 Jordan theorem 62
§4.3 Uniqueness 66
§4.4 Convex representation 70
§4.5 Notes 76
Chapter 5. Planarity 77
§5.1 Immersions 77
§5.2 Wu Tutte theorem 81
§5.3 Planarity auxiliary graphs 86
§5.4 The main theorems 91
§5.5 Notes .....:. .97
Chapter 6. Gauss Crossing Problem 99
§6.1 Crossing sequences 99
§6.2 Dehn s theorem 103
§6.3 Gauss conjecture 109
§6.4 Notes 115
Chapter 7. Planar Embeddings 117
§7.1 Left and right determinations 117
§7.2 Forbidden configurations 122
§7.3 Basic order characterization 129
§7.4 Number of planar embeddings 137
§7.5 Notes 143
Chapter 8. Rectilinear Embeddability 144
§8.1 Rectilinear embeddings 144
§8.2 Tri embeddability 151
§8.3 Bi embeddability 161
§8.4 Uni embeddability 168
§8.5 Notes 175
Contents XV
Chapter 9. Net Embeddability 177
§9.1 Admissibility 177
§9.2 Corner sequences 183
§9.3 General criterion 190
§9.4 Special criteria 196
§9.5 Notes 203
Chapter 10. Isomorphisms in Polyhedra 205
§10.1 Automorphims of polyhedra 205
§10.2 Eulerian and non Eulerian codes 210
§10.3 Isomorphisms in polyhedra 219
§10.4 Notes 225
Chapter 11. Decompositions of Graphs 227
§11.1 Biconnected decomposition 227
§11.2 Triconnected decomposition 231
§11.3 Planar decomposition 237
§11.4 The page decomposition 243
§11.5 Rectilinear Decomposition 248
§11.6 Notes 252
Chapter 12. Surface Embeddability 255
§12.1 Necessary conditions 255
§12.2 Up embeddability 260
§12.3 Quotient embeddings 265
§12.4 Down embeddability 273
§12.5 Notes 281
Chapter 13. Extremal Problems 284
§13.1 Optimal convex embeddings 284
§13.2 Shortest triangulations 290
xvj Contents
§13.3 Minimal bend embeddings 295
§13.4 Minimal area embeddings 302
§13.5 Notes .308
Chapter 14. Graphic and Cographic Matroids 310
§14.1 Binary matroids 310
§14.2 Regularity 315
§14.3 Graphicness 321
§14.4 Notes 328
Chapter 15. Invariants on Knots 330
§15.1 Knot types 330
§15.2 Graphic models 334
§15.3 Invariants 340
§15.4 Notes 350
References 352
Index 388
|
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| id | DE-604.BV010783190 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T17:58:49Z |
| institution | BVB |
| isbn | 7030047729 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007202312 |
| oclc_num | 32855528 |
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| owner_facet | DE-12 DE-703 DE-83 |
| physical | XVI, 398 S. graph. Darst. |
| publishDate | 1995 |
| publishDateSearch | 1995 |
| publishDateSort | 1995 |
| publisher | Science Press [u.a.] |
| record_format | marc |
| series2 | Mathematics and its application, China series |
| spelling | Liu, Yanpei Verfasser aut Embeddability in graphs Liu Yanpei Beijing Science Press [u.a.] 1995 XVI, 398 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Mathematics and its application, China series This monograph provides a theoretical treatment of the problems related to the embeddability of graphs. Among these problems are the planarity and planar embeddings of a graph, the Gaussian crossing problem, the isomorphisms of polyhedra, surface embeddability, problems concerning graphic and cographic matroids and the knot problem from topology to combinatorics are discussed. Rectilinear embeddability, and the net-embeddability of a graph, which appears from the VSLI circuit design and has been much improved by the author recently, is also illustrated. Furthermore, some optimization problems related to planar and rectilinear embeddings of graphs, including those of finding the shortest convex embedding with a boundary condition and the shortest triangulation for given points on the plane, the bend and the area minimizations of rectilinear embeddings, and several kinds of graph decompositions are specially described for conditions efficiently solvable At the end of each chapter, the Notes Section sets out the progress of related problems, the background in theory and practice, and some historical remarks. Some open problems with suggestions for their solutions are mentioned for further research Embeddings (Mathematics) Graph theory Einbettung Mathematik (DE-588)4151233-9 gnd rswk-swf Graph (DE-588)4021842-9 gnd rswk-swf Graph (DE-588)4021842-9 s Einbettung Mathematik (DE-588)4151233-9 s DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007202312&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Liu, Yanpei Embeddability in graphs Embeddings (Mathematics) Graph theory Einbettung Mathematik (DE-588)4151233-9 gnd Graph (DE-588)4021842-9 gnd |
| subject_GND | (DE-588)4151233-9 (DE-588)4021842-9 |
| title | Embeddability in graphs |
| title_auth | Embeddability in graphs |
| title_exact_search | Embeddability in graphs |
| title_full | Embeddability in graphs Liu Yanpei |
| title_fullStr | Embeddability in graphs Liu Yanpei |
| title_full_unstemmed | Embeddability in graphs Liu Yanpei |
| title_short | Embeddability in graphs |
| title_sort | embeddability in graphs |
| topic | Embeddings (Mathematics) Graph theory Einbettung Mathematik (DE-588)4151233-9 gnd Graph (DE-588)4021842-9 gnd |
| topic_facet | Embeddings (Mathematics) Graph theory Einbettung Mathematik Graph |
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