Given a graph G=(V,E) with capacities on edges let us call an edge e, critical if an increase in c_e increases the value of the maximal s-t flow. a. Build a (nontrivial) network that has no critical edges b. Give an efficient algorithm to find all critical eges of the graph. Hint: residual graph.

They have another proof on chegg but that does not make sense to or provide proof of correctness or time complexity.