Exact complexity class of Eternal-Dominating-Number

Determine the exact computational complexity class of the decision problem Eternal-Dominating-Number: given a graph G and an integer k ≥ 1, decide whether the eternal domination number γ∞(G) satisfies γ∞(G) ≤ k.

Background

The paper defines the Eternal-Dominating-Number decision problem and recalls known bounds and algorithms on special classes. It is known that Eternal-Domininating-Number lies in EXP and is coNP-hard, but its precise placement within standard complexity classes is unresolved.

Resolving the exact complexity class would clarify whether the problem is complete for a particular class (e.g., EXP, PSPACE, coNP, Σ2^P) or perhaps admits a more efficient algorithmic characterization than currently known.