Planarity – Can you find the planar embedding?

agree, cool 14 moves but 87 seconds ;-)

If you know the graph is planar, then you can find the Tutte embedding by solving a set of linear equations [1].

However, the problem of finding a drawing that minimises the number of edge crossings (or even just the number of crossings in such a layout [e.g., 2]) for a general graph is NP-hard.

[1]: https://en.wikipedia.org/wiki/Tutte_embedding

[2]: https://epubs.siam.org/doi/abs/10.1137/120872310

There are linear time algorithms that take a planar graph and find an embedding where all the edges are straight lines.

However, I believe the problem of starting with a general graph and finding an embedding with the minimum number of edge crossings is NP-Hard.