Disjoint shortest paths in graphs

It is an interesting problem that how much connectivity ensures the existence ofn disjoint paths joining givenn pairs of vertices, but to get a sharp bound seems to be very difficult. In this paper, we study how muchgeodetic connectivity ensures the existence ofn disjointgeodesics joining givenn pairs of vertices, where a graph is calledk-geodetically connected if the removal of anyk−1 vertices does not change the distance between any remaining vertices.