Combinatorial properties of polyominoes

descriptionPublicationkeyboard_double_arrow_right Article 01 Sep 1981 English Publisher:Springer Science and Business Media LLCJournal:Combinatorica, volume 1, pages 217-224 (issn: 0209-9683, eissn: 1439-6912,

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Authors: Claude Berge 0001; C. C. Chen; Vasek Chvátal; C. S. Seow;

doi: 10.1007/bf02579327

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.

Related Organizations

Nanyang Technological University
Singapore
McGill University
Canada

Keywords

transversal, Edge subsets with special properties (factorization, matching, partitioning, covering and packing, etc.), Polyominoes, maximal rectangles, semiconvexity, Hypergraphs, largest clique

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