Domino Tatami Covering is NP-complete

A covering with dominoes of a rectilinear region is called \emph{tatami} if no four dominoes meet at any point. We describe a reduction from planar 3SAT to Domino Tatami Covering. As a consequence it is NP-complete to decide whether there is a perfect matching of a graph that meets every 4-cycle, even if the graph is restricted to be an induced subgraph of the grid-graph. The gadgets used in the reduction were discovered with the help of a SAT-solver.Comment: 10 pages, accepted at The International Workshop on Combinatorial Algorithms (IWOCA) 201

NP-completeness of the game Kingdomino

Kingdomino is a board game designed by Bruno Cathala and edited by Blue Orange since 2016. The goal is to place $2 \times 1$ dominoes on a grid layout, and get a better score than other players. Each $1 \times 1$ domino cell has a color that must match at least one adjacent cell, and an integer number of crowns (possibly none) used to compute the score. We prove that even with full knowledge of the future of the game, in order to maximize their score at Kingdomino, players are faced with an NP-complete optimization problem

Jezyki Obce w Szkole Nr 4/2008

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