The per-degree fractional perfect-matching conjecture for r-graphs

Let $G$ be an $r$-graph. A $(t,r)$-PM is a multiset of $t\cdot r$ perfect matchings of $G$ such that every edge of $G$ is contained in exactly $t$ of them. The per-degree fractional perfect-matching conjecture. For every $r\geq 1$ there is a $t_r\geq 1$ such that every $r$-graph has a $(t_r,r)$-PM. This is a weaker version of the generalized Berge–Fulkerson conjecture, and the source states that the relevant reductions remain open.