Cutting down recursive trees

Abstract A recursive tree is constructed by starting with a source node and repeatedly adjoining new nodes to one node of the tree already constructed. Such a tree could represent, for example, the spread of contamination from a single source within some organism. If we remove an edge from such a tree it falls into two subtrees one of which contains the source. If we continue to remove edges from the successively smaller subtrees that contain the source we eventually isolate the source. We consider how many randomly selected edges must be removed on the average before isolating the source by this procedure.