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.

Graphs are collections of nodes connected by edges. They can be used to represent everything from a social network to road systems to the electrical connections on a circuit board. In circuit boards, ...

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, ...

Problem 1: Find a subquadratic algorithm for testing if a given graph is 1-planar. It is also easy to check in cubic time if G is 2-apex by testing planarity of all 2-vertex-deleted subgraphs. More ...