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Leaving aside the trivial case (graphs which only have one $r$-arborescence), this won't be possible. Suppose $(V,E)$ is an $r$-arborescence of $(V,A)$. Then $E$ contains some (nonzero) number of arcs $(r,s_1),\ldots,(r,s_k)$ out of the root (otherwise we are in a trivial case). Now if $(V,F)$ is another arborescence, then either $F$ also contains some $(r,...


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