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 ...

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 ...

Now imagine that you want to insert a new edge connecting two nodes in a planar graph, say nodes 1 and 6 in the example below. To do so, you’re going to perform a series of flips. From the starting ...

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 ...

Let G be any n-vertex planar graph. We prove that the vertices of G can be partitioned into three sets A, B, C such that no edge joins a vertex in A with a vertex in B, neither A nor B contains more ...

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 ...