Monophonic-position problem complexity

Determine whether the Monophonic Position Set problem is NP-complete for general graphs.

Background

The Monophonic Position Set problem is known to be NP-hard, including on diameter-two graphs. However, the survey notes that NP-completeness for general graphs is unresolved because polynomial-time verification of a proposed solution has not been established.

References

However, it is not clear whether the {\sc Monophonic Position Set} is NP-complete for general graphs, since proving this would also require demonstrating that a solution can be verified in polynomial time.

— The General Position Problem: A Survey  (2501.19385 - V. et al., 31 Jan 2025) in Section 5, subsection “Monophonic position sets”