Graph colouring remains a central topic in graph theory, providing the mathematical framework for assigning colours to the elements of a graph under specific constraints. In particular, the colouring ...

If G is a planar graph, we may add edges to construct a maximal planar graph H containing G, so that H triangulates the sphere. If G is toroidal, then by adding edges we can extend G to a maximal ...

Jacob Holm was flipping through proofs from an October 2019 research paper he and colleague Eva Rotenberg—an associate professor in the department of applied mathematics and computer science at the ...

We prove that given any sequence $G_1, G_2,\ldots$ of graphs, where $G_1$ is finite planar and all other $G_i$ are possibly infinite, there are indices $i,j$ such ...