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Combinatorial properties of polyominoes

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Abstract

A finite set of cells in the infinite planar square grid is often called a polyomino. With each polyominoP, we may associate a hypergraph whose vertices are the cells ofP and whose edges are the maximal rectangles (in the standard position) contained inP. It turns out that these hypergraphs have many nice properties generalizing various properties of bipartite graphs and trees. We survey results in this direction.

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References

  1. C. Berge,Graphs and hypergraphs, North-Holland, Amsterdam, 1973.

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  2. S. Chaiken, D. J. Kleitman, M. Saks andJ. Shearer, Covering regions by rectangles,SIAM J. Discrete and Algebraic Methods, to appear.

  3. S. W. Golomb,Polyominoes, Charles Scribner’s Sons, New York, 1965.

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Authors and Affiliations

  1. C. N. R. S. Paris, France

    C. Berge

  2. Nanyang University, Singapore

    C. C. Chen

  3. McGill University, Montreal

    V. Chvátal

  4. Nanyang University, Singapore

    C. S. Seow

Authors
  1. C. Berge
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  2. C. C. Chen
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  3. V. Chvátal
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  4. C. S. Seow
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Berge, C., Chen, C.C., Chvátal, V. et al. Combinatorial properties of polyominoes. Combinatorica 1, 217–224 (1981). https://doi.org/10.1007/BF02579327

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  • DOI: https://doi.org/10.1007/BF02579327

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