The study of such graphs is called graph theory. Engineers need to find planarity in a graph when, for example, they are designing a computer chip without a crossed wire.

Now imagine that you want to insert a new edge connecting two nodes in a planar graph, say nodes 1 and 6 in the example below. To do so, you’re going to perform a series of flips. From the starting ...

A classic example, the Four Colour Theorem, illustrates a fundamental property of planar graphs, while recent advancements have extended these ideas to more specialised variants, including list ...