Beyond-Planar Graphs: Models, Structures and Geometric Representations (Dagstuhl Seminar 24062)

This report documents the program and the outcomes of Dagstuhl Seminar 24062 "Beyond-Planar Graphs: Models, Structures and Geometric Representations". The seminar investigated beyond-planar graphs, in particular, their combinatorial and topological structures, computational complexity and algorithmics for recognition, geometric representations, and their applications to real-world network visualization. Compared to the previous two editions of the seminar, we focus more on aspects of combinatorics and geometry. The program consists of four invited talks on beyond planar graphs, open problem session, problem solving sessions and progress report sessions. Specific open problems include questions regarding the combinatorial structures and topology (e.g., k^+-real face graphs, beyond upward planar graphs, sparse universal geometric graphs, local-crossing-critical graphs), the geometric representations (e.g., constrained outer string graphs, rerouting curves on surface), and applications. The details of the invited talks and progress reports from each working groups are included in this report.