A prominent attempt to extend the rich body of knowledge from planar to non-planar graphs has emerged within the context of beyond-planarity, a compelling area of research that has garnered considerable attention in recent years. This line of research provides a systematic and natural generalization of planarity, encompassing several graph families that, in various well-defined ways, exhibit properties closely related to planarity. Among the numerous graph classes investigated within this context, the following have emerged as the most extensively studied:

• k-planar graphs, in which each edge is crossed at most k times.
• k-quasiplanar graphs, which disallow k pairwise crossing edges.
• fan-planar graphs, in which edges that cross the same edge should be adjacent.
• RAC graphs, in which edge crossings only happen at right angles.

In this line of research, our research group has received funding from the Hellenic Foundation for Research and Innovation (from 2025 to 2029) to advance the research along the following research directions.