PSPACE-completeness on planar directed graphs

Establish that Rooted Partizan Edge Geography and Rooted Distinct Partizan Edge Geography remain PSPACE-complete on planar directed graphs of maximum degree 3.

Background

The paper proves PSPACE-completeness for Rooted Partizan Edge Geography and its distinct-token variant on bipartite undirected graphs of maximum degree 3. Since ordinary Geography is already known to be PSPACE-complete on planar directed graphs of maximum degree 3, the authors explicitly conjecture that the corresponding directed planar restriction also preserves PSPACE-completeness for both problems studied in the paper.

References

Geography is known to be PSPACE-complete on planar directed graphs with maximum degree 3. We conjecture that the two problems in this paper remains PSPACE-complete on such graphs.

— The Complexity of Undirected Partizan Edge Geography  (2609.18330 - Okada, 16 Sep 2026) in Section Conclusions