Combinatorial properties of polyominoes

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

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

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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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AMS subject classification (1980)

  • 05 C 70
  • 05 B 50
  • 05 C 65