Infinite graphs with induced Euclidean copies

Characterize the infinite graphs that admit an induced unit-copy in some finite-dimensional Euclidean space, and determine whether the associated induced Ramsey function grows with dimension for every such graph.

Background

The paper proves a lower bound for finite and certain infinite multipartite graphs, but its induced asymptotic argument does not extend directly to infinite graphs.

References

What is the necessary and sufficient condition for an infinite graph $H$ to have an induced unit-copy in $n$ for some $n$? Does ${n}{H}$ grow with $n$ for such graphs?

— Ramsey problems for graphs in Euclidean spaces and Cartesian powers  (2512.15516 - Axenovich et al., 17 Dec 2025) in Question Q_inf_induced, Section 6.3 (Infinite graphs)