1-orderable acyclic graph families

Construct an infinite family of acyclic directed graphs that are 1-orderable, or prove that no such family exists.

Background

The paper establishes that every inner-connected graph has finite pp-rank and that acyclic graphs are inner-connected. It also gives examples of 1-orderable acyclic graphs, but the largest example found has only twelve edges. The authors suspect that only finitely many acyclic graphs are 1-orderable, making the existence of an infinite family unresolved.

References

Find a family of 1-orderable acyclic graphs, or show that there is none.

— Graphs with Bounded Push-Pop Walk Orderings  (2610.19724 - Amarilli et al., 14 Oct 2026) in Appendix, Section “Open Problems,” subsection “Lower Bounds”