# Why graph planarity is important

What is the reason to study planar graphs and algorithms on such graphs (as well as algorithms allowing to check a graph's planarity)? Where in industry this knowlege is needed? I know that planarity arises in microchip design ("wires" intersection). I also found the following excerpt from a lecture notes:

The study of two-dimensional images often results in problems related to planar graphs, as does the solution of many problems on the two-dimensional surface of our earth. Many natural three-dimensional graphs arise in scientific and engineering problems. These often come from well-shaped meshes, which share many properties with planar graphs.

Where I can read about it in more detail? Or may be you can explain in a few words what exactly these applications are?

For some graph classes $C$, the question "is there a fast algorithm for deciding whether a graph $G$ belongs to class $C$?" is perhaps only of theoretical curiosity. But it can also be argued otherwise: suppose a problem you care about is hard in general, but efficiently solvable for graphs of class $C$. Wouldn't it be nice if you could quickly test if you can use a fast algorithm, instead of always using a slow brute-force, for example?