On the Computational Complexities of Various Geography Variants
Abstract
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 winner 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.
Keywords
Cite
@article{arxiv.2108.09367,
title = {On the Computational Complexities of Various Geography Variants},
author = {Nathan Fox and Carson Geissler},
journal= {arXiv preprint arXiv:2108.09367},
year = {2021}
}
Comments
39 pages, 1 table, 16 figures