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 ...

Lawler, Schramm and Werner showed that the scaling limit of the loop-erased random walk on ℤ 2 is SLE 2 . We consider scaling limits of the loop-erasure of random walks on other planar graphs (graphs ...

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 ...