Strong Target Conjecture

Let $G$ be a graph, let $D$ be a target, let $|D|$ denote its total demand, and let $s(D)$ denote the parameter used in the source.

Strong Target Conjecture. Every graph $G$ satisfies

$$\pi(G,D)\leq \pi_{|D|}(G)-s(D)+1$$

for every target $D$.

The source reports that this stronger inequality is known for trees and powers of paths, but remains unproved for general graphs.