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

TL;DR

This paper proves that Misère Partizan Arc Kayles is PSPACE-complete on planar graphs by reducing from Bounded Two-Player Constraint Logic and demonstrates embedding these gadgets onto common grid graphs.

Contribution

It establishes the PSPACE-completeness of Misère Partizan Arc Kayles on planar graphs and introduces new PSPACE-complete variants of Bounded Two-Player Constraint Logic.

Findings

Misère Partizan Arc Kayles is PSPACE-complete on planar graphs.

Embedded gadgets onto square and triangular grids.

Identified three PSPACE-complete variants of Bounded Two-Player Constraint Logic.

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.