When you understand the algorithm, you can write the C code.

That's the point. The video you send didn't have any algorithms. She only talks about the theorem and it only states that a finite graph is planar if and only if it does not contain a subgraph that is a subdivision of k5 or k3,3. The video doesn't tell you how to know if a graph is or isn't a subdivision of k5 or k3,3. It's just a basic introduction to the graph theory which I said that I already know.

There's a tiny bit of math (if you could call it that) to set things up, then they show graphs, then show pseudo code to explain it. When you understand it, you code it in the language of your choice.

Are you talking about the Numberphile video? Or the papers? If it's the video then as I said above it doesn't contain any "pseudo code". If you're talking about the papers then can I ask you a couple of questions about those algorithms?

If you can't find anything on something for games, its because game devs haven't used it.

Not really. I only want to know "How to find a planar embedding of a graph and draw it on a grid" which is a pretty general question in computer science about graph theory. There isn't anything specific to game development. I'm just having a hard time understanding these papers and couldn't find any youtube videos about the topic (there are only videos about basic introduction to graph theory).