Geometric graphs and arrangements: some chapters from combinatorial geometry
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Wiesbaden
Vieweg
2004
|
| Edition: | first edition |
| Series: | Advanced lectures in mathematics
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | X, 170 Seiten Illustrationen, Diagramme |
| ISBN: | 3528069724 |
Staff View
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| 245 | 1 | 0 | |a Geometric graphs and arrangements |b some chapters from combinatorial geometry |c Stefan Felsner |
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Record in the Search Index
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| adam_text | Contents
Preface V
Contents IX
1 Geometric Graphs: Turan Problems 1
1.1 What is a Geometric Graph? 1
1.2 Fundamental Concepts in Graph Theory 2
1.3 Planar Graphs 3
1.4 Outerplanar Graphs and Convex Geometric Graphs 6
1.5 Geometric Graphs without (k + 1) Pairwise Disjoint Edges 7
1.6 Geometric Graphs without Parallel Edges 10
1.7 Notes and References 13
2 Schnyder Woods or How to Draw a Planar Graph? 17
2.1 Schnyder Labelings and Woods 17
2.2 Regions and Coordinates 23
2.3 Geodesic Embeddings of Planar Graphs 24
2.4 Dual Schnyder Woods 28
2.5 Order Dimension of 3 Polytopes 30
2.6 Existence of Schnyder Labelings 35
2.7 Notes and References 37
3 Topological Graphs: Crossing Lemma and Applications 43
3.1 Crossing Numbers 43
3.2 Bounds for the Crossing Number 44
3.3 Improving the Crossing Constant 46
3.4 Crossing Numbers and Incidence Problems 48
3.5 Notes and References 50
4 fc Sets and fc Facets 53
4.1 fc Sets in the Plane 53
4.2 Beyond the Plane 58
4.3 The Rectilinear Crossing Number of Kn 61
4.4 Notes and References 66
5 Combinatorial Problems for Sets of Points and Lines 69
5.1 Arrangements, Planes, Duality 69
5.2 Sylvester s Problem 72
5.3 How many Lines are Spanned by n Points? 76
5.4 Triangles in Arrangements 78
5.5 Notes and References 84
X Contents
6 Combinatorial Representations of Arrangements of Pseudolines 87
6.1 Marked Arrangements and Sweeps 87
6.2 Allowable Sequences and Wiring Diagrams 91
6.3 Local Sequences 95
6.4 Zonotopal Tilings 100
6.5 Triangle Signs 105
6.6 Signotopes and their Orders 108
6.7 Notes and References Ill
7 Triangulations and Flips 114
7.1 Degrees in the Flip Graph 114
7.2 Delaunay Triangulations 117
7.3 Regular Triangulations and Secondary Polytopes 120
7.4 The Associahedron and Catalan families 123
7.5 The Diameter of Qn and Hyperbolic Geometry 125
7.6 Notes and References 129
8 Rigidity and Pseudotriangulations 131
8.1 Rigidity, Motion and Stress 131
8.2 Pseudotriangles and Pseudotriangulations 139
8.3 Expansive Motions 143
8.4 The Polyhedron of of Pointed Pseudotriangulations 144
8.5 Expansive Motions and Straightening Linkages 148
8.6 Notes and References 149
Bibliography 151
Index 165
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| discipline | Mathematik |
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| indexdate | 2024-07-09T18:42:33Z |
| institution | BVB |
| isbn | 3528069724 |
| language | English |
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| physical | X, 170 Seiten Illustrationen, Diagramme |
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| spelling | Felsner, Stefan aut Geometric graphs and arrangements some chapters from combinatorial geometry Stefan Felsner first edition Wiesbaden Vieweg 2004 X, 170 Seiten Illustrationen, Diagramme txt rdacontent n rdamedia nc rdacarrier Advanced lectures in mathematics Kombinatorische Geometrie - Lehrbuch Kombinatorische Geometrie (DE-588)4140733-7 gnd rswk-swf (DE-588)4123623-3 Lehrbuch gnd-content Kombinatorische Geometrie (DE-588)4140733-7 s DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009034051&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Felsner, Stefan Geometric graphs and arrangements some chapters from combinatorial geometry Kombinatorische Geometrie - Lehrbuch Kombinatorische Geometrie (DE-588)4140733-7 gnd |
| subject_GND | (DE-588)4140733-7 (DE-588)4123623-3 |
| title | Geometric graphs and arrangements some chapters from combinatorial geometry |
| title_auth | Geometric graphs and arrangements some chapters from combinatorial geometry |
| title_exact_search | Geometric graphs and arrangements some chapters from combinatorial geometry |
| title_full | Geometric graphs and arrangements some chapters from combinatorial geometry Stefan Felsner |
| title_fullStr | Geometric graphs and arrangements some chapters from combinatorial geometry Stefan Felsner |
| title_full_unstemmed | Geometric graphs and arrangements some chapters from combinatorial geometry Stefan Felsner |
| title_short | Geometric graphs and arrangements |
| title_sort | geometric graphs and arrangements some chapters from combinatorial geometry |
| title_sub | some chapters from combinatorial geometry |
| topic | Kombinatorische Geometrie - Lehrbuch Kombinatorische Geometrie (DE-588)4140733-7 gnd |
| topic_facet | Kombinatorische Geometrie - Lehrbuch Kombinatorische Geometrie Lehrbuch |
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