Extension to the m-eternal (all guards move) variant

Ascertain whether the algorithms and complexity results obtained for Fast-Strategy extend to the m-eternal domination variant in which the Defender may move more than one guard per turn, and characterize the minimal number of turns required for Attacker to win in this setting.

Background

The m-eternal domination (all guards move) variant generalizes the defender’s mobility. While upper bounds on the number of moves are known in some cases (e.g., trees), it is unclear whether the paper’s methods and positive results (trees, cographs) adapt to this broader model.

Addressing this would unify understanding across eternal domination variants and might require novel techniques to handle simultaneous guard movements.