# Domino Tatami Covering is NP-complete

@article{Erickson2013DominoTC,
title={Domino Tatami Covering is NP-complete},
author={Alejandro Erickson and Frank Ruskey},
journal={ArXiv},
year={2013},
volume={abs/1305.6669}
}
• Published 28 May 2013
• Mathematics
• ArXiv
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.
5 Citations

### Tatami Maker: A combinatorially rich mechanical game board

A modular, mechanical game board is described, prototyped with a desktop 3D printer, that enforces tatami pen-and- paper puzzles into interactive sculptures and presents five new combinatorial games implemented on the game board.

### NP-completeness of the game Kingdomino

• Computer Science
ArXiv
• 2019
It is proved 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.

## References

SHOWING 1-10 OF 15 REFERENCES

### Complexity of Cycle Transverse Matching Problems

• Mathematics
IWOCA
• 2011
This paper investigates the problem of determining whether a graph contains a matching that meets every copy of H, and shows that the problem for C3 is polynomial and for each Cl with l≥4 is NP-complete.

### The complexity of domino tiling

This paper studies domino tiling with a constant number of colours, and shows that this problem of how to tile a layout with dominoes is NP-hard even with 3 colours.

### Enumerating maximal tatami mat coverings of square grids with $v$ vertical dominoes

• Mathematics
• 2013
We enumerate a certain class of monomino-domino coverings of square grids, which conform to the \emph{tatami} restriction; no four tiles meet. Let $\mathbf T_{n}$ be the set of monomino-domino tatami

### Counting Fixed-Height Tatami Tilings

• Mathematics
Electron. J. Comb.
• 2009
This work presents and uses Dean Hickerson's combinatorial decomposition of the set of tatami tilings — a decomposition that allows them to be viewed as certain classes of restricted compositions when $n \ge m$ and uses it to verify a modified version of a conjecture of Knuth.

### Rectilinear planar layouts and bipolar orientations of planar graphs

Discret. Comput. Geom.
• 1986
This work proposes a linear-time algorithm, a variant of one by Otten and van Wijk, that generally produces a more compact layout than theirs and allows the dual of the graph to be laid out in an interlocking way.

### Tiling layouts with dominoes

• Mathematics
CCCG
• 2004
The authors show that the problem of tiling a ribbon, which is an infinite “path” in the plane, is undecidable and provide an time algorithm for tiling layouts that are paths or cycles.

### On a Problem of Marco Buratti

• Mathematics
Electron. J. Comb.
• 2009
This work considers a problem formulated by Marco Buratti concerning Hamiltonian paths in the complete graph on Z_p, an odd prime, and its application to graph analysis.

### Planar Formulae and Their Uses

Using these results, it is able to provide simple and nearly uniform proofs of NP-completeness for planar node cover, planar Hamiltonian circuit and line, geometric connected dominating set, and of polynomial space completeness forPlanar generalized geography.

### Monomer-Dimer Tatami Tilings of Rectangular Regions

• Mathematics
Electron. J. Comb.
• 2011
This paper provides a structural characterization and uses it to prove that the tiling is completely determined by the tiles that are on its border, and proves that the number of tatami tilings of an n-1 square with monomers is n2^{n-1}\$.

### The Computational Complexity of the Kakuro Puzzle, Revisited

• Computer Science
FUN
• 2010
A new proof of NP-completeness for the problem of solving instances of the Japanese pencil puzzle KAKURO (also known as Cross-Sum), and some parts of the proof have been generated automatically, using an interesting technique involving SAT solvers.