Seymour's non-uniform Caccetta–Häggkvist conjecture

Let $D$ be a simple digraph with no sink, meaning no vertex has outdegree zero. Define

$$\psi(D)=\sum_{v\in V(D)}\frac{1}{\deg^+(v)}.$$

Seymour's non-uniform Caccetta–Häggkvist conjecture. $D$ contains a directed cycle of length at most

$$\left\lceil\psi(D)\right\rceil.$$

When all outdegrees equal $r$, this would imply the Caccetta–Häggkvist conjecture. The conjecture was disproved by Hompe, so it is refuted.