Planar Graph

Planar graphs, graphs that can be drawn on a plane without edge crossings, are a central topic in graph theory with applications ranging from mapmaking to network design. Current research focuses on understanding the computational complexity of problems on planar graphs, such as finding optimal solutions for multi-agent pathfinding and graph partitioning (e.g., gerrymandering), and developing efficient algorithms and neural network architectures for tasks like graph generation and representation learning. These advancements contribute to a deeper understanding of fundamental graph-theoretic problems and offer improved tools for tackling real-world challenges in areas like logistics, network optimization, and computational biology.