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 ...

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 ...

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 ...

W. T. Tutte, A Theorem on Planar Graphs, Transactions of the American Mathematical Society, Vol. 82, No. 1 (May, 1956), pp. 99-116 ...

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 ...