graph planarity testing

Graph planarity testing is a method used to determine whether a graph can be drawn on a flat surface without any of its edges crossing. Imagine connecting dots (vertices) with lines (edges); if you can do this without any lines overlapping except at the dots, the graph is planar. Algorithms for planarity testing analyze the structure of the graph efficiently to identify such possibilities. This concept is important in fields like network design and circuit layout, where avoiding crossing connections can simplify construction and improve clarity.