Domino Tatami Covering Is NP-Complete

  • Alejandro Erickson
  • Frank Ruskey
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8288)


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.


Boolean Formula Horizontal Edge Satisfying Assignment Domino Tiling Variable Gadget 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Alejandro Erickson
    • 1
  • Frank Ruskey
    • 1
  1. 1.Department of Computer ScienceUniversity of VictoriaCanada

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