, the bipartite graph associated to D (see previous Section 2). Hence, ? +,? (D) ? 2 if and only if ? ? (B(D)) ? 2. As proved by Thomassen, Wu and Zhang [15], a connected bipartite graph G verifies ? ? (G) ? 2 if and only if G is not an odd multicactus, a class of 2-degenerate 2-connected graphs that can be constructed and recognized easily. Now, since constructing B(D) from D can be done in polynomial time, and checking whether a bipartite graph is an odd multicactus can also be done in polynomial time (see [15] for more details), the claim follows. We now prove the result in Row "? + = ? +, As observed in [1], finding a (+, ?)-distinguishing k-arc-weighting of D is equivalent to finding a neighbour-sum-distinguishing k-edge-weighting of B(D)

. .. ?????-vu-d-+-;, By v(p i ), we mean the value of the element p i is currently pointing at in L i . Assuming p i is not pointing at the largest element of L i , by moving p i to the right, we mean making p i point at the first element of L i that is larger than the one it is currently pointing at. Start from each p i pointing at the smallest element of L i . The first sum we consider is v, The proof is by induction on the number of arcs in D. Since the claim can easily be verified by hand for digraphs with only a few arcs

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