Geometric Graphs and Arrangements: Some Chapters from Combinatorial Geometry

✍ Scribed by Prof. Dr. Stefan Felsner (auth.)

• Publisher: Vieweg+Teubner Verlag
• Year: 2004
• Tongue: English
• Leaves: 178
• Series: Advanced Lectures in Mathematics
• Edition: 1
• Category: Library

✦ Synopsis

Among the intuitively appealing aspects of graph theory is its close connection to drawings and geometry. The development of computer technology has become a source of motivation to reconsider these connections, in particular geometric graphs are emerging as a new subfield of graph theory. Arrangements of points and lines are the objects for many challenging problems and surprising solutions in combinatorial geometry. The book is a collection of beautiful and partly very recent results from the intersection of geometry, graph theory and combinatorics.

✦ Table of Contents

Front Matter....Pages I-X
Geometric Graphs: Turán Problems....Pages 1-16
Schnyder Woods or How to Draw a Planar Graph?....Pages 17-42
Topological Graphs: Crossing Lemma and Applications....Pages 43-52
k -Sets and k -Facets....Pages 53-68
Combinatorial Problems for Sets of Points and Lines....Pages 69-86
Combinatorial Representations of Arrangements of Pseudolines....Pages 87-113
Triangulations and Flips....Pages 114-130
Rigidity and Pseudotriangulations....Pages 131-150
Back Matter....Pages 151-170

✦ Subjects

Geometry; Algebra