English

On the Computational Complexities of Various Geography Variants

Computational Complexity 2021-08-24 v1 Combinatorics

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

R2 v1 2026-06-24T05:17:48.887Z