This is a preview. Log in through your library . Abstract This paper investigates the group testing problem in graphs as follows. Given a graph G = (V, E), determine the minimum number t(G) such that ...

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 ...

Let us say that a graph is k-apex if it contains a set of at most k vertices whose removal yields a planar graph. We define the apex number of a graph G as the minimum k for which G is k-apex. It is ...