We are given a flow network $G = (V,E,c)$, where $c$ is the capacity function as well as a maximum flow $f_m: E\rightarrow \mathbb R$ from $s$ to $t$. The goal is to find edges such that if decreased by one unit, the value of any max flow decreases as well. The time complexity should be $O(VE)$.
I found this question in my algorithm book.
My attempt: I thought all saturated edges could satisfy this condition. Then I found some counterexamples.