We prove NP-completeness of Yin-Yang / Shiromaru-Kuromaru pencil-and-paper puzzles. Viewed as a graph partitioning problem, we prove NP-completeness of partitioning a rectangular grid graph into two induced trees (normal Yin-Yang), or into two induced connected subgraphs (Yin-Yang without $2 \times 2$ rule), subject to some vertices being pre-assigned to a specific tree/subgraph.

中文翻译：

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阴阳拼图是 NP 完全的

我们证明了阴阳/白丸黑丸纸笔拼图的 NP 完备性。从图划分问题来看，我们证明了将矩形网格图划分为两个诱导树（正常阴阳）或两个诱导连通子图（没有 $2 \times 2$ 规则的阴阳）的 NP 完备性，受制于一些顶点被预先分配给特定的树/子图。