A classic example, the Four Colour Theorem, illustrates a fundamental property of planar graphs, while recent advancements have extended these ideas to more specialised variants, including list ...

• Each example shows the graph, its metrics, and an explanation of why it’s planar or not. Learn • Educational content on planar graph theory: definitions, Euler’s formula, Kuratowski’s theorem, and ...

However, the main source of inspiration for planar graphs was the Four Color Conjecture (now Theorem; cf. Chapter 8) that the vertices of any planar graph can be colored with four colors in such a way ...

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 ...

The facilities layout problem is concerned with laying out facilities on a planar site in order to design systems that are as efficient as possible. One approach to the problem involves the use of REL ...

Planar Cable-Driven Parallel Robots (CDPRs) offer significant advantages in various applications, but their deployment has been limited due to challenges in setup and calibration. In this paper, we ...