Hoang–Reed conjecture on cycles with small overlaps

Let $r\in\mathbb{N}$, and let $\delta^+(D)$ denote the minimum out-degree of a digraph $D$. A sequence $C_1,\ldots,C_r$ of directed cycles has at most one overlap per cycle if, for each $i$, the $i$th cycle shares at most one vertex with the union of its predecessors. Hoang–Reed conjecture. Every digraph $D$ with

$$\delta^+(D)\ge r$$

contains a sequence $C_1,\ldots,C_r$ of directed cycles such that, for each $i\in [r]$,

$$\left|V(C_i)\cap \bigcup_{1\le j<i}V(C_j)\right|\le 1.$$

The conjecture remains open and would directly imply the Caccetta–Häggkvist conjecture.