The important insight is that for repetition codes, this results in what's called a planar graph, where edges don't cross each other. "This allows us to exploit the exact, efficient solutions for ...

When slicing a model for 3D printing, the part is divided into a stack of flat, 2D layers. But there’s an alternative in the form of non-planar slicing, where the layers can follow 3D curves. [Rene K.

If G is a planar graph, we may add edges to construct a maximal planar graph H containing G, so that H triangulates the sphere. If G is toroidal, then by adding edges we can extend G to a maximal ...

Let us say that a graph is k-apex if it contains a set of at most k vertices whose removal yields a planar graph. We define the apex number of a graph G as the minimum k for which G is k-apex. It is ...