1. The problem statement, all variables and given/known data Here is an exercise I came across while studying MaxFlow / MinCut and I'm rather stumped: Designate G = (V, E) as an undirected graph that has at least two vertices. Every edge e on this graph has capacity ce. Pick two arbitrary vertices from G and label them s and t respectively. Now, we'll let P* be the set of s-t paths in the graph, and let C* be the set of s-t cuts -- meaning, C* refers to the subset of edges in G that constitute all possible s-t cuts. Demonstrate that the following equality is true: maxP∈P* mine∈P ce = minC∈C* maxe∈C ce 2. Relevant equations Size of Max Flow = Min. Capacity of an s-t Cut 3. The attempt at a solution My issue: I'm having trouble parsing the above equation. The LHS appears to be describing the longest(?) of all possible s-t paths, and the edge with the minimum capacity along that path. The RHS appears to be describing the minimum number of edges(?) possible in a subset of edges constituting an s-t cut, and the edge with the max. capacity within that subset? I'm frankly not even sure whether the above equation is meant to involve a multiplication. Still, I figure there must be a way to parse and understand the equation correctly such that the equality would always hold, and that it can be demonstrated as such. I'd appreciate any help in this matter.