Asymptotic spanning trees in finitely generated Cayley graphs

Determine whether every finitely generated Cayley graph has an asymptotic spanning tree.

Background

The paper observes that its asymptotic spanning-tree questions have natural Cayley graph analogues. It asks whether every finitely generated Cayley graph admits the corresponding coarse spanning structure.

References

Does every finitely generated Cayley graph\ have an ?

— Asymptotic connectivity, hamiltonicity and toughness  (2610.09992 - Georgakopoulos, 7 Oct 2026) in Problem, Section 1, subsection “Spanning trees”