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 ...

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 ...

Two computer scientists found — in the unlikeliest of places — just the idea they needed to make a big leap in graph theory. This past October, as Jacob Holm and Eva Rotenberg were thumbing through a ...