Question: 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

Given a graph G (V, E), and a natural number k,

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 & V, we say that x y if there exist k mutually edge-disjoint paths from x to y in G Is it true that for every G and every k 2 0, the relation is transitive? That is, is it always the case that if x? y and y? z, then we have x?z? Give a proof or a counterexample. G,k G.k G.R

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