NP-completeness of the stress convexity number decision problem

Determine whether, for every fixed positive integer k, deciding whether the stress convexity number cs(G) of a graph G is at most k is NP-complete.

Background

The stress convexity number cs(G) is defined as the order of a largest proper stress-convex subgraph of G. The paper notes that analogous convexity-number decision problems are NP-complete for several other graph convexities. It leaves unresolved whether the corresponding decision problem for stress convexity has the same complexity.

References

In many other well-known graph convexities, deciding whether the convexity number is at most k (where k ∈ N) is NP-complete [17, 18]. Does this also hold for s-convexity? Question 3. Is it true that for a given k ∈ N, deciding whether cs(G) ≤ k is NP-complete problem?

— On the stress transit function  (2502.09153 - Anil et al., 13 Feb 2025) in Question 3, Section 5, page 15