Question: Let L = (a1, b1), . . . , (ak, bk) be the k pairs of distinct labels ai, bi {1, . . .

Let L = (a1, b1), . . . , (ak, bk) be the k pairs of distinct labels ai, bi ∈ {1, . . . , n}. Consider now a complete network of n nodes; in this network, select 2k + 1 nodes x0, x1, , . . . , x2k. Show that it is always possible 1. to label the links between these nodes only with pairs from L (e.g., the link

(x0, x1) will be labeled a3 at x0 and b3 at x1), and 2. to label all others links in the network with labels in {1, . . . , n} without violating local orientation anywhere.

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