Note on the diameter of path-pairable graphs

A graph on 2k2k vertices is path-pairable if for any pairing of the vertices the pairs can be joined by edge-disjoint paths. The so far known families of path-pairable graphs have diameter of at most 3. In this paper we present an infinite family of path-pairable graphs with diameter d(G)=O(n) where nn denotes the number of vertices of the graph. We prove that our example is extremal up to a constant factor.