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Dagstuhl Seminar 24062

Beyond-Planar Graphs: Models, Structures and Geometric Representations

( Feb 04 – Feb 09, 2024 )

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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.

This Dagstuhl Seminar will investigate beyond-planar graphs, in particular, their combinatorial and topological structures (i.e., density, thickness, crossing pattern, chromatic number, queue number, and stack number), computational complexity and algorithmics for recognition, geometric representations (i.e., straight-line drawing, polyline drawing, intersection graphs), and their applications to real-world network visualization. Behind the fundamental scientific challenges and significant advances of this seminar lies the pragmatic need for effective visualization algorithms of real-world big complex networks.

Copyright Vida Dujmovic, Seok-Hee Hong, Michael Kaufmann, and János Pach


Related Seminars
  • Dagstuhl Seminar 16452: Beyond-Planar Graphs: Algorithmics and Combinatorics (2016-11-06 - 2016-11-11) (Details)
  • Dagstuhl Seminar 19092: Beyond-Planar Graphs: Combinatorics, Models and Algorithms (2019-02-24 - 2019-03-01) (Details)

  • Computational Geometry
  • Data Structures and Algorithms
  • Discrete Mathematics

  • Graph drawing
  • Graph algorithm
  • Graph theory
  • Combinatorial geometry
  • Network visualization