Strict EKR robustness beyond trivial actions

Determine whether there exist nontrivial group actions other than regular and Frobenius actions that are strict EKR robust.

Background

The paper introduces strict EKR robustness as the property that the independence number remains the star size unless all derangements mapping some point i to j and their inverses have been removed. Regular and Frobenius representations satisfy this property for essentially trivial structural reasons, while the existence of other examples remains unresolved.

References

It is open if there are other, more interesting, group actions that are strict EKR robust.

— A new measure of robustness of Erdős--Ko--Rado Theorems on permutation groups  (2502.14582 - Gunderson et al., 20 Feb 2025) in Section 7, paragraph preceding Conjecture 7.8