Determining the uniqueness of a min-cut

Question

Disclaimer: this was a homework problem. The deadline has passed now, so discussions can continue without needing to worry about that.

The

Answer 1

Given that max flow/min cut problem is really a Linear programming problem(primal/dual respectively), I reckon any method to check uniqueness of LP solution and finding alternative optimum solution if its not unique can be used in this context. I googled to find this paper :On the Uniqueness of Solutions to Linear Programs EDIT 1: Based on suggestion by dzhuang, for those who are unaware that maxflow-mincut theorem is a special case of strong duality theorem in linear programming, here is the link explaining this nuance: https://en.wikipedia.org/wiki/Max-flow_min-cut_theorem#Linear_program_formulation