Cubic-graph monophonic position number

Determine the asymptotic maximum monophonic position number of cubic graphs of order \(n\), specifically whether it is \(n/3+O(n)\).

Background

The monophonic position number is defined using induced paths rather than shortest paths. Computational evidence led to a conjecture concerning the largest possible monophonic position number among cubic graphs.

References

The largest possible monophonic position number of a cubic graph with order $n$ is $\frac{n}{3}+O(n)$.

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