Polynomial-time solvability of the Normal Domination Game on trees

Characterize the class of trees on which the Normal Domination Game is polynomial-time solvable, specifically determine whether the Normal Domination Game is polynomial-time solvable on all trees.

Background

The paper establishes PSPACE-completeness of the Normal Domination Game on general graphs and gives efficient algorithms for paths, cycles, and disjoint unions of these graphs. The authors state that they have not fully characterized the class of trees and pose the unresolved question of polynomial-time solvability on trees.

References

We were unfortunately unable to fully characterize the class of trees. For instance, \begin{question} The Normal Domination Game is polynomial time solvable in trees? \end{question}

— The Normal Play of the Domination Game  (2502.13118 - Brito et al., 18 Feb 2025) in Section 'Conclusions and Open Problems'