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
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.