Given a graph G = (V, E), and a natural number k, we can define a relation  on pairs of ve...

Given a graph G = (V, E), and a natural number k, we can define a relation  on pairs of vertices of G as follows. If x, y ε V, we say that  if there exist k mutually edge-disjoint paths from x to y in G.

Is it true that for every G and every k ≥ 0, the relation is transitive? That is, is it always the case that if  and , then we have  Give a proof or a counterexample.