Graphs with Geometric Representations

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The interplay of graphs and geometric representations has two aspects that lead to different types of problem. Type 1, is to start withsome graph and ask whether he admits a representation in a prescribed model of geometric realization. Type 2, is to start with a geometric configuration and ask about properties of some graphs induced by the configuration. In the proposed project we are interested in problems of both types. To group them we establish two research areas I. Geometric representations of planar graphs. II. Intersection representations and order. Each areas has three subareas. We have grouped problems from each of the subareas that are to be addressed within the project. Some of the problems are well known and assumed to be hard. Their solution will have impact for other fields.