Polynomial-time computation of the stress hull number

Determine whether a polynomial-time algorithm exists for computing the stress hull number of an arbitrary graph.

Background

The stress hull number is the minimum size of a set whose stress-convex hull contains every vertex of the graph. The paper computes this invariant for several graph families, but does not establish the computational complexity of finding it for general graphs. The authors explicitly identify the existence of a polynomial-time algorithm as unresolved.

References

For some special graph families, we obtained exact values also for the stress hull number, but we do not know how hard is the problem of computing the stress hull number of general graph. Question 2. Is there a polynomial-time algorithm that computes the stress hull number of a graph G?

— On the stress transit function  (2502.09153 - Anil et al., 13 Feb 2025) in Question 2, Section 5, page 15