Ebook: Geometric Graphs and Arrangements: Some Chapters from Combinatorial Geometry

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.

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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.

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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.
Content:
Front Matter....Pages I-X
Geometric Graphs: Tur?n 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

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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.
Content:
Front Matter....Pages I-X
Geometric Graphs: Tur?n 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
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