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 ...

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 ...

When adding a new edge to a planar graph is required, there are two scenarios: There is a safe way to add the edge, possibly after modifying the drawing, or no drawing admitting the edge exists.

The term "minimal nonplanar subgraph" of a graph G refers to a nonplanar subgraph N of G having the property that each proper subgraph of N is planar. A well-known result of graph theory is that there ...

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 ...

"While the QEC community knew planar graphs simplified MLE decoding, few recognized MLD could also be efficient for such topologies. This insight directly motivated our work," they explained.

It is easy to check in quadratic time if a graph is 1-apex - simply test for each vertex v, if G - v is planar. Problem 1: Find a subquadratic algorithm for testing if a given graph is 1-planar. It is ...