The separating-set characterization of unlinkable webs

Let $\Gamma$ be a web, and let $A$ and $B$ be its distinguished vertex sets. An $A$--$B$-separating set $S$ meets every $A$--$B$ path; $S$ is linkable into $A$ in $\overleftarrow{\Gamma}$ when the reversed web contains a linkage from $S$ to $A$, and $A$ is linkable into $S$ in $\Gamma$ analogously. Separating-set characterization conjecture. If $\Gamma$ is unlinkable, then there exists an $A$--$B$-separating set $S$ which is linkable into $A$ in $\overleftarrow{\Gamma}$, but $A$ is not linkable into $S$ in $\Gamma$. The text presents this as a third formulation equivalent to the Erdős–Menger conjecture.