Orthogonal-tree representation criterion

Characterize the graphs that admit an induced unit-copy in an orthogonal copy of some tree.

Background

The paper verifies that all graphs on at most four vertices admit such a representation and identifies three five-vertex exceptions, but no general characterization is known.

References

What is the necessary and sufficient condition for a graph to admit an induced unit-copy in an orthogonal copy of some tree?

— Ramsey problems for graphs in Euclidean spaces and Cartesian powers  (2512.15516 - Axenovich et al., 17 Dec 2025) in Question, Appendix B, Section B.2 (Orthogonal trees)