Dagstuhl-Seminar — Beyond-Planar Graphs: Models, Structures and Geometric Representations

Many big data sets in various application domains have complex relationships, which can be modelled as graphs, consisting of entities and relationships between them. Consequently, graphs are extensively studied in both Mathematics and Computer science. In particular, planar graphs, which can be drawn without edge crossings in the plane, form a distinguished role in Graph Theory and Graph Algorithms. Many structural properties of planar graphs are investigated, in terms of excluded minors, low density, and small separators, which lead to efficient algorithms for planar graphs. Consequently, fundamental algorithms for planar graphs have been discovered. However, most real-world graphs, such as social networks and biological networks, are nonplanar. For example, the scale-free networks, which are used to model web graphs, social networks and biological networks, are globally sparse nonplanar graphs, with locally dense clusters and low diameters. To understand such real-world networks, we need to solve fundamental mathematical and algorithmic research questions on beyond-planar graphs, which generalize the notion of planar graphs, in terms of topological constraints or forbidden edge crossing patterns.