Verstraëte's conjecture on packing graph subdivisions

Given graphs $F$ and $G$, a subdivision packing of $F$ in $G$ is a collection of pairwise vertex-disjoint copies of subdivisions of $F$. For a real number $\eta > 0$ and a graph $F$, let $d_0=d_0(F,\eta)$ be a threshold degree. Verstraëte's conjecture. For every graph $F$ and every $\eta>0$, there exists $d_0=d_0(F,\eta)$ such that, for every integer $d\ge d_0$, every $d$-regular graph $G$ of order $n$ contains a subdivision packing covering all but at most $\eta n$ vertices of $G$. This conjecture concerns approximate spanning packings in dense regular graphs; the paper establishes stronger perfect-packing results when the degree is linear in the order of the graph.