Sum-Networks: Min-Cut = 2 Does Not Guarantee Solvability

In this paper, we consider sum-networks where each terminal requires sum of all the sources. For a sum-network having 3 sources and 3 terminals, it is known that the network is solvable if the min-cut between each source and each terminal is at least 2. However, it is not known whether this condition is sufficient for sum-networks having arbitrary number of sources and terminals. In the present work, we present a sum-network which is not solvable even though the min-cut between any source and any terminal is at least 2.