In collaboration with

• TU Berlin,

• TU Graz and

• ETH Zürich.

Arrangements of geometric objects and drawings of graphs are fundamental concepts at the core of discrete and computational geometry. They are of great importance in both computer science and mathematics and serve as a crucial tool in applications. Many important problems that involve geometric information are problems on arrangements or graphs. Also, many seemingly unrelated questions can be stated as problems on arrangements or graphs. Therefore, the study of these structures and their better understanding impacts a wide variety of problem domains. The list of prominent open problems in discrete mathematics contains several basic problems on arrangements and graphs. Solving such problems is of great theoretical interest and will certainly influence future directions of research in discrete mathematics and computational geometry.

The importance of the research area Geometric Graphs can be seen from the fact that in 2010 the European Science Foundation (ESF) made a call for outline proposals within the European Collaborative Research Programme (EUROCORES) on the topic ”Graphs in Geometry and Algorithms” (EuroGIGA). Consequently, four different Collaborative Research Projects (CRPs) have been supported by countries all over Europe. In the final consensus report of EuroGIGA, two out of the four CRPs were classified as their achievements being outstanding, namely, GraDr and ComPoSe.

This DACH project aims to combine and extend research groups from both GraDr and ComPoSe in a follow-up project to focus on some core areas from these two CRPs. In particular, we plan to investigate the relationships between different types and abstract representations of drawings and planar arrangements and their algorithmic properties.