NP-Completeness of the minimum edge-ranking spanning tree problem on series-parallel graphs

The minimum edge-ranking spanning tree (MERST) problem on a graph is to find a spanning tree of G whose edge-ranking needs least number of ranks. Although polynomial-time algorithm to solve the minimum edge-ranking spanning tree problem on series-parallel graphs with bounded degrees has been found, but for the unbounded degrees no polynomial-time algorithm is known. In this paper, we prove that the minimum edge-ranking spanning tree problem on general series-parallel graph is NP-complete.