Mis\`ere Partizan Arc Kayles is PSPACE-complete, even on Planar Graphs
Computational Complexity
2025-12-01 v1 Discrete Mathematics
Combinatorics
Abstract
We show that Mis\`ere Partizan Arc Kayles is PSPACE-complete on planar graphs via a reduction from Bounded Two-Player Constraint Logic. Furthermore, we show how to embed our gadgets onto the square and triangular grids. In order to clearly explain these results, we get into the details of Bounded Two-Player Constraint Logic and find three PSPACE-complete variants of that as well.
Keywords
Cite
@article{arxiv.2511.21888,
title = {Mis\`ere Partizan Arc Kayles is PSPACE-complete, even on Planar Graphs},
author = {Kyle Burke and Caroline Cashman and Alfie Davies and Kanae Yoshiwatari and Francesca Yu},
journal= {arXiv preprint arXiv:2511.21888},
year = {2025}
}
Comments
21 pages, 23 figures