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

The Langberg-M'{e}dard multiple unicast conjecture claims that for a strongly 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 {\em stable} $3$-pair networks.