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We give a simple proof of that determining solvability of Shisen-Sho boards is NP-complete. Furthermore, we show that under realistic assumptions, one can compute in logarithmic time if two tiles form a playable pair. We combine an implementation of the algoritm to test playability of pairs with my earlier algorithm to solve Mahjong Solitaire boards with peeking, to obtain an algorithm to solve Shisen-Sho boards. We sample several Shisen-Sho and Mahjong Solitaire layouts for solvability for Shisen-Sho and Mahjong Solitaire.
A bipartite graph $G=(A,B,E)$ is ${cal H}$-convex, for some family of graphs ${cal H}$, if there exists a graph $Hin {cal H}$ with $V(H)=A$ such that the set of neighbours in $A$ of each $bin B$ induces a connected subgraph of $H$. Many $mathsf{NP}$-
}We study (vertex-disjoint) $P_2$-packings in graphs under a parameterized perspective. Starting from a maximal $P_2$-packing $p$ of size $j$ we use extremal arguments for determining how many vertices of $p$ appear in some $P_2$-packing of size $(j+
A vertex subset $I$ of a graph $G$ is called a $k$-path vertex cover if every path on $k$ vertices in $G$ contains at least one vertex from $I$. The textsc{$k$-Path Vertex Cover Reconfiguration ($k$-PVCR)} problem asks if one can transform one $k$-pa
We show how two techniques from statistical physics can be adapted to solve a variant of the notorious Unique Games problem, potentially opening new avenues towards the Unique Games Conjecture. The variant, which we call Count Unique Games, is a prom
In this paper we study the family of two-state Totalistic Freezing Cellular Automata (TFCA) defined over the triangular and square grids with von Neumann neighborhoods. We say that a Cellular Automaton is Freezing and Totalistic if the active cells r