Planar Graph: A graph that can be drawn on a plane without any edges crossing. Graph Colouring: The process of assigning colours to elements of a graph, typically vertices, so that adjacent ...

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 ...

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 ...

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 ...

Research demonstrating that planar graphs without 4-cycles adjacent to triangles are DP-4-colourable has provided a valuable extension of previous list colouring results, thereby establishing ...