On the Computational Complexities of Various Geography Variants

Nathan Fox; Carson Geissler

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arXiv · 2108.09367

On the Computational Complexities of Various Geography Variants

Nathan Fox·Carson Geissler

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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.

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Nathan Fox, Carson Geissler. 2021-08-20. On the Computational Complexities of Various Geography Variants. https://arxiv.org/abs/2108.09367

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