Universal finite generation for homology of graph configuration spaces

Let $F_n(G)$ be the configuration space of $n$ ordered points in a graph $G$. For a class of graphs, universal finite generation in degree $i$ and with $n$ particles means that a finite collection of graphs generates $H_i(F_n(G))$ for every graph in the class via classes arising from topological subgraphs homeomorphic to members of that collection. Universal finite generation conjecture. Universal finite generation holds for the class of all graphs. This is the main finiteness conjecture for homology of graph configuration spaces; the paper explains that it would follow from the categorical graph minor and categorical Robertson conjectures, and records supporting results in several special cases.