Optimizing Geometric Graphs

Projekt: Forschungsprojekt



The general topic of this project is the investigation of geometric graphs, i.e., graphs where the vertex set is a point set in the plane and the edges are straight line segments spanned by these points. Throughout we assume the points to be in general position, that is no three of them lie on a common line, and to be labeled. Geometric graphs are a versatile data structure, as they include triangulations, Euclidean spanning trees, spanning paths, polygonalizations, plane perfect matchings and so on. The investigation of geometric graphs belongs to the field of (combinatorial) mathematics, graph theory, as well as to discrete and computational geometry. The alliance of our two research groups will perfectly cover these fields. For example this will allow us to use an interesting combination of enumerative investigations (lead by the Austrian team) and theoretical research (coordinated by the Spanish group). Let us point out that this combination of theoretical knowledge and practical experience, which is perfectly provided by the combination of these two teams, will be essential for the success of this project. There are many classic as well as new tantalizing problems on geometric graphs, and the investigation of seemingly unrelated questions often leads to new relations and deeper structural insight. So the focus of this project is to investigate several classes of problems with the common goal of optimizing properties of geometric graphs.
Tatsächlicher Beginn/ -es Ende1/01/0831/12/09


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