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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.
In the Nikoli pencil-and-paper game Tatamibari, a puzzle consists of an $m times n$ grid of cells, where each cell possibly contains a clue among +, -, |. The goal is to partition the grid into disjoint rectangles, where every rectangle contains exac
When can $t$ terminal pairs in an $m times n$ grid be connected by $t$ vertex-disjoint paths that cover all vertices of the grid? We prove that this problem is NP-complete. Our hardness result can be compared to two previous NP-hardness proofs: Lynch
Using the probability theory-based approach, this paper reveals the equivalence of an arbitrary NP-complete problem to a problem of checking whether a level set of a specifically constructed harmonic cost function (with all diagonal entries of its He
Holzer and Holzer (Discrete Applied Mathematics 144(3):345--358, 2004) proved that the Tantrix(TM) rotation puzzle problem with four colors is NP-complete, and they showed that the infinite variant of this problem is undecidable. In this paper, we st
We show that the decision problem of determining whether a given (abstract simplicial) $k$-complex has a geometric embedding in $mathbb R^d$ is complete for the Existential Theory of the Reals for all $dgeq 3$ and $kin{d-1,d}$. This implies that the