  Very recently, a long-standing open question proposed by Bodlaender in 1991
was answered: the graph coloring game is PSPACE-complete. In 2019, Andres and
Lock proposed five variants of the graph coloring game and left open the
question of PSPACE-hardness related to them. In this paper, we prove that these
variants are PSPACE-complete for the graph coloring game and also for the
greedy coloring game, even if the number of colors is the chromatic number.
Finally, we also prove that a connected version of the graph coloring game,
proposed by Charpentier et al. in 2019, is PSPACE-complete.
