On the Computational Complexities of Various Geography Variants [article]

Nathan Fox, Carson Geissler
2021 arXiv   pre-print
Generalized Geography is a combinatorial game played on a directed graph. Players take turns moving a token from vertex to vertex, deleting a vertex after moving the token away from it. A player unable to move loses. It is well known that the computational complexity of determining which player should win from a given position of Generalized Geography is PSPACE-complete. We introduce several rule variants to Generalized Geography, and we explore the computational complexity of determining the
more » ... nner of positions of many resulting games. Among our results is a proof that determining the winner of a game known in the literature as Undirected Partizan Geography is PSPACE-complete, even when restricted to being played on a bipartite graph.
arXiv:2108.09367v1 fatcat:jvxhhowttvhd5d3szbk33rupui