Graph colouring remains a central topic in graph theory, providing the mathematical framework for assigning colours to the elements of a graph under specific constraints. In particular, the colouring ...

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 ...

Abstract: In this paper, a four-color coloring algorithm for maximal planar graphs with finite boundary is proposed, which aims to explore the four-color coloring method for complex planar graphs.

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 ...

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 ...

Abstract Modern acquisition techniques generate detailed point clouds that sample complex geometries. For instance, we are able to produce millimeter-scale acquisition of whole buildings. Processing ...