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The Langberg-M\'{e}dard multiple unicast conjecture claims that for astrongly reachable $k$-pair network, there exists a multi-flow with rate$(1,1,\dots,1)$. In this paper, we show that the conjecture holds true for {\emstable} $3$-pair networks.

The Langberg-M\'{e}dard Multiple Unicast Conjecture: Stable $3$-Pair Networks