Length 3 Edge-Disjoint Paths and Partial Orientation

In 2003, it was claimed that the following problem was solvable in polynomial time: do there exist k edge-disjoint paths of length exactly 3 between vertices s and t in a given graph? The proof was flawed, and we show that this problem is NP-hard even if we disallow multiple edges. We use a reduction from Partial Orientation, a problem recently shown by Pálvölgyi to be NP-hard. In [2], Bley discussed the problem Max Edge-Disjoint Exact-l-Length Paths, abbreviated MEDEP(l): given an undirected multigraph, and two vertices s and t, do there exist k edge-disjoint paths between s and t of length exactly l? He used a reduction to network flow to claim that MEDEP(3) was solvable in polynomial time, but the reduction was flawed, as we describe in [1], where we also showed that MEDEP(3) is NP-hard. For completeness we duplicate the proof below, as Theorem 1. In this note, we show that the problem MEDEP(3) remains NP-hard even if we require the input graph to be simple. We call this restricted problem Simple