On the capacity of multiple unicast sessions in undirected graphs

Li and Li conjectured that in an undirected network with multiple unicast sessions, network coding does not lead to any coding gain. Surprisingly enough, this conjecture could not so far be verified even for the simple network consisting of K
_3,2
with four source-sink pairs. Using entropy calculus, we provide the first verification of the Li-Li conjecture for this network. We extend our bound to the case of an arbitrary directed bipartite network