Geometric Graphs and Arrangements: Some Chapters from Combinatorial Geometry

ISBN-13: 9783528069728 / Angielski / Miękka / 2004 / 170 str.

Opis

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 mostly very recent results from the intersection of geometry, graph theory and combinatorics.

Recenzje

"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

Spis treści

Geometric Graphs: Turán Problems - Schnyder Woods or How to Draw a Planar Graph? - Topological Graphs: Crossing Lemma and Applications- k-Sets and k-Facets - Combinatorial Problems for Sets of Points and Lines - Combinatorial Representations of Arrangements of Pseudolines - Triangulations and Flips - Rigidity and Pseudo-Triangulations

O autorze

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

Blurb

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.