Biclique Reconfiguration in Bipartite Graphs

TL;DR

This paper establishes the PSPACE-completeness of various reconfiguration problems in bipartite graphs, resolving open questions and extending known complexity results in graph reconfiguration theory.

Contribution

It proves PSPACE-completeness of Balanced Biclique Reconfiguration and related problems, advancing the understanding of computational complexity in graph reconfiguration.

Findings

Balanced Biclique Reconfiguration is PSPACE-complete.

Spanning variant of Subgraph Reconfiguration is PSPACE-complete.

Connected Components Reconfiguration with two components is PSPACE-complete.

Abstract

We prove that Balanced Biclique Reconfiguration on bipartite graphs is PSPACE-complete. This implies the PSPACE-completeness of the spanning variant of Subgraph Reconfiguration under the token jumping rule for the property "a graph is an $(i, j)$-complete bipartite graph," which was previously known only to be NP-hard [Hanaka et al. TCS 2020]. Using our result, we also show that Connected Components Reconfiguration with two connected components is PSPACE-complete under all previously studied rules, resolving an open problem of Nakahata [COCOON 2025] in the negative.