Stefan Felsner

Geometric Graphs and Arrangements

Some Chapters from Combinatorial Geometry

• Broschiertes Buch

Produktbeschreibung

Das Ziel dieses Lehrbuches in englischer Sprache ist es, einige faszinierende neue Entwicklungen aus dem Grenzbereich von Geometrie, Graphentheorie und Kombinatorik darzustellen. Dieses Gebiet ist sowohl für Mathematiker als auch für Informatiker von hohem Interesse. Der Text wird durch sehr viele Abbildungen erläutert und abgerundet.

Produktdetails

• Advanced Lectures in Mathematics
• Verlag: Vieweg
• Artikelnr. des Verlages: 978-3-528-06972-8
• Softcover reprint of the original 1st ed. 2004
• Seitenzahl: 184
• Erscheinungstermin: 24. Februar 2004
• Englisch
• Abmessung: 240mm x 170mm x 11mm
• Gewicht: 360g
• ISBN-13: 9783528069728
• ISBN-10: 3528069724
• Artikelnr.: 08652054

Autorenporträt

Prof. Dr. Stefan Felsner, Institut für Mathematik, Technische Universität Berlin, Germany.

Inhaltsangabe

1 Geometric Graphs: Turán Problems.- 1.1 What is a Geometric Graph?.- 1.2 Fundamental Concepts in Graph Theory.- 1.3 Planar Graphs.- 1.4 Outerplanar Graphs and Convex Geometric Graphs.- 1.5 Geometric Graphs without (k + 1)-Pairwise Disjoint Edges.- 1.6 Geometric Graphs without Parallel Edges.- 1.7 Notes and References.- 2 Schnyder Woods or How to Draw a Planar Graph?.- 2.1 Schnyder Labelings and Woods.- 2.2 Regions and Coordinates.- 2.3 Geodesic Embeddings of Planar Graphs.- 2.4 Dual Schnyder Woods.- 2.5 Order Dimension of 3-Polytopes.- 2.6 Existence of Schnyder Labelings.- 2.7 Notes and References.- 3 Topological Graphs: Crossing Lemma and Applications.- 3.1 Crossing Numbers.- 3.2 Bounds for the Crossing Number.- 3.3 Improving the Crossing Constant.- 3.4 Crossing Numbers and Incidence Problems.- 3.5 Notes and References.- 4 k-Sets and k-Facets.- 4.1 k-Sets in the Plane.- 4.2 Beyond the Plane.- 4.3 The Rectilinear Crossing Number of Kn.- 4.4 Notes and References.- 5 Combinatorial Problems for Sets of Points and Lines.- 5.1 Arrangements, Planes, Duality.- 5.2 Sylvester's Problem.- 5.3 How many Lines are Spanned by n Points?.- 5.4 Triangles in Arrangements.- 5.5 Notes and References.- 6 Combinatorial Representations of Arrangements of Pseudolines.- 6.1 Marked Arrangements and Sweeps.- 6.2 Allowable Sequences and Wiring Diagrams.- 6.3 Local Sequences.- 6.4 Zonotopal Tilings.- 6.5 Triangle Signs.- 6.6 Signotopes and their Orders.- 6.7 Notes and References.- 7 Triangulations and Flips.- 7.1 Degrees in the Flip-Graph.- 7.2 Delaunay Triangulations.- 7.3 Regular Triangulations and Secondary Polytopes.- 7.4 The Associahedron and Catalan families.- 7.5 The Diameter of Gn and Hyperbolic Geometry.- 7.6 Notes and References.- 8 Rigidity and Pseudotriangulations.- 8.1 Rigidity,Motion and Stress.- 8.2 Pseudotriangles and Pseudotriangulations.- 8.3 Expansive Motions.- 8.4 The Polyhedron of of Pointed Pseudotriangulations.- 8.5 Expansive Motions and Straightening Linkages.- 8.6 Notes and References.

Rezensionen

"The book is written in a pleasant and clear style, with generous pictures and lucid explanations. [...] I recommend this splendid litte book für PhD students and researchers who work or wish to work in discrete geometry".
Combinatorics, Probability and Computing (Cambridge University Press), 15/2006

"[The author] has contributed an introduction to this fascinating and mathematically challenging - yet intuitively accessible - field."
Monatshefte für Mathematik, 02/2006