Highly connected uniquely $k$-linked digraphs

Abstract

Extending a result of Thomassen, we prove that for every choice of positive integers $K\ge k$ there exist a $K$-strong digraph which has two disjoint sets $S,T$ each of size $k$ so that the only linkage from $S$ to $T$ in $D$ is the one whose existence follows from Menger's theorem.