Conjecture: Fast-Strategy is PSPACE-complete on bipartite graphs

Prove or refute that Fast-Strategy (given a graph G, a set of guards D ⊆ V(G), and an integer t ≥ 1, decide whether t_G(D) ≤ t) is PSPACE-complete on bipartite graphs.

Background

The paper shows Fast-Strategy is coNP-hard on bipartite graphs and PSPACE-hard on certain perfect (2-unipolar) graphs. Given that many game-like graph problems tend to be either polynomial-time or PSPACE-hard, the authors conjecture the stronger PSPACE-completeness for bipartite graphs.

Settling this conjecture would pinpoint the precise complexity on bipartite graphs, aligning it with other combinatorial game problems and clarifying the algorithmic limits for this class.