Domino Tatami Covering is NP-complete

  title={Domino Tatami Covering is NP-complete},
  author={Alejandro Erickson and Frank Ruskey},
A covering with dominoes of a rectilinear region is called 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 therefore 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. 

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