Complexity of the stress set problem on chordal graphs

Determine the time complexity of the stress set problem on chordal graphs, given that the problem is NP-complete for general graphs but solvable in polynomial time for split graphs.

Background

The stress set problem asks whether a graph has a stress set of cardinality at most a specified integer. The paper proves that this decision problem is NP-complete even for bipartite graphs and establishes polynomial-time computability of the stress number for split and block graphs. Since chordal graphs form a superclass of split graphs, the authors explicitly leave the complexity classification for chordal graphs unresolved.

References

Given that the problem is NP-complete for general graphs but solvable in polynomial time for split graphs, we pose the following question regarding their superclass—the well-known chordal graphs. Question 1. What is the time complexity of the stress set problem in chordal graphs?

— On the stress transit function  (2502.09153 - Anil et al., 13 Feb 2025) in Question 1, Section 5, page 15