Planar graph algorithms constitute a pivotal area in theoretical computer science, addressing problems where graphs can be drawn on a plane without edge crossings. Among the myriad challenges in this ...

Two computer scientists found — in the unlikeliest of places — just the idea they needed to make a big leap in graph theory. This past October, as Jacob Holm and Eva Rotenberg were thumbing through a ...

Graphs are everywhere. In discrete mathematics, they are structures that show the connections between points, much like a ...

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 ...

A new algorithm corrects connection points of objects fabricated by wire bending machine to optimize stability, say investigators. During the annual top conference of the Special Interest Group for ...