Thomas's half-integral Erdős–Pósa conjecture for graph minors

Let $H$ be a graph. A graph $G$ half-integrally packs $k$ graphs if it contains subgraphs isomorphic to those graphs such that every vertex of $G$ belongs to at most two of the subgraphs. A graph $G$ contains $H$ as a minor if $H$ can be obtained from a subgraph of $G$ by vertex and edge contractions.

Thomas's conjecture. For every graph $H$, there exists a function $f$ such that for every graph $G$ and every positive integer $k$, either $G$ half-integrally packs $k$ graphs each containing $H$ as a minor, or there exists a set $Z\subseteq V(G)$ with $\lvert Z\rvert\leq f(k)$ such that $G-Z$ does not contain $H$ as a minor.

This conjecture extends the Erdős–Pósa property for graph minors from integral to half-integral packing, potentially removing the planarity restriction on $H$. The source presents it as a conjecture of Thomas; its resolution is not specified here.