Finite universal generators conjecture for graph configuration-space homology

Let $\mathcal{G}$ be a collection of graphs. Say that $\mathcal{G}$ is a set of universal generators in degree $i$ if, for every graph $\mathsf{\Gamma}$, the group $H_i(F_k(\mathsf{\Gamma});\mathbb{Z})$ is generated by homology classes arising from topological subgraphs homeomorphic to members of $\mathcal{G}$. Finite universal generators conjecture. A finite set of universal generators exists in every degree. Partial results identify universal generators in several settings, while the paper identifies disjoint unions of stars as asymptotic universal generators. The existence of a finite generating set in every degree remains open.