The weighted maximal planar graph (WMPG) is practically important in the laying out of facilities in modern manufacturing environments. Given a weighted complete graph, the WMPG seeks to find a ...

A new technical paper titled “Fabrication of graphene field effect transistors on complex non-planar surfaces” was published by researchers at Imperial College London. “Graphene field effect ...

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 ...

When you’re spitting out G-Code for a 3D print, you can pick all kinds of infill settings. You can choose the pattern, and the percentage… but the vast majority of slicers all have one thing in common ...

A graph is planar if it can be drawn in the plane in such a way that no edges intersect, except of course at a common endvertex. Planar graphs corresponding to the regular polyhedra and other ...

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 ...