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arXiv · 1708.06063

Helly Numbers of Polyominoes

Jean Cardinal·Hiro Ito·Matias Korman·Stefan Langerman
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Abstract

We define the Helly number of a polyomino $P$ as the smallest number $h$ such that the $h$-Helly property holds for the family of symmetric and translated copies of $P$ on the integer grid. We prove the following: (i) the only polyominoes with Helly number 2 are the rectangles, (ii) there does not exist any polyomino with Helly number 3, (iii) there exist polyominoes of Helly number $k$ for any $k\neq 1,3$.

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Jean Cardinal, Hiro Ito, Matias Korman, Stefan Langerman. 2017-08-21. Helly Numbers of Polyominoes. https://doi.org/10.1007/s00373-012-1203-x

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