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.

翻译：我们证明，二分图上的均衡双团重配问题（Balanced Biclique Reconfiguration）是PSPACE-完全的。这一结果蕴含了在令牌跳跃规则下，关于性质"图是一个$(i,j)$-完全二分图"的生成子图重配（spanning variant of Subgraph Reconfiguration）问题的PSPACE-完全性，而此前该问题仅已知为NP-难[Hanaka等，TCS 2020]。基于我们的结论，我们还证明，在之前研究的所有规则下，具有两个连通分量的连通分量重配问题（Connected Components Reconfiguration）是PSPACE-完全的，从而否定了Nakahata [COCOON 2025]提出的一个开放问题。