Finite Hamilton-cover conjecture for two-ended transitive graphs

Let $\Gamma$ be a two-ended transitive graph. A finite Hamilton cover is a finite collection of Hamiltonian spanning subgraphs whose union covers the relevant graph structure, as in the source's preceding discussion. Hamilton-cover conjecture. Every two-ended transitive graph has a finite Hamilton cover. The conjecture is motivated by constructions producing Hamilton double rays, Hamilton circles, and infinite Hamilton covers in two-ended Cayley graphs; its status is not resolved in the source.