Finding the two-core of a tree

The l-core of a graph is a path minimizing the sum of the distances of all vertices of the graph from the path. A linear algorithm for finding a l-core of a tree was presented by Morgan and Slarer. The problem for general graphs is NP-hard. A 2-core of a graph is a set of IWO paths minimizing the sum of the distances of all vertices of the graph from any of the two paths. We consider both cases of disjoint paths and intersecting paths for a tree. s