Thomassen's theorem on the two-linkage problem in acyclic digraphs: A shorter proof

Abstract

Let G be an acyclic digraph, and let $a,b,c,d\in V\left(G\right)$, where $a,b$ are sources, $c,d$ are sinks, and every other vertex has in-degree and out-degree at least two. In 1985, Thomassen showed that there do not exist disjoint directed paths from a to c and from b to d, if and only if G can be drawn in a closed disc with $a,b,c,d$ drawn in the boundary in order. We give a shorter proof.