Mis\`ere Partizan Arc Kayles is PSPACE-complete, even on Planar Graphs

Kyle Burke; Caroline Cashman; Alfie Davies; Kanae Yoshiwatari; Francesca Yu

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arXiv · 2511.21888

Mis\`ere Partizan Arc Kayles is PSPACE-complete, even on Planar Graphs

Kyle Burke·Caroline Cashman·Alfie Davies·Kanae Yoshiwatari·Francesca Yu

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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.

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Kyle Burke, Caroline Cashman, Alfie Davies, Kanae Yoshiwatari, Francesca Yu. 2025-11-26. Mis\`ere Partizan Arc Kayles is PSPACE-complete, even on Planar Graphs. https://arxiv.org/abs/2511.21888

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