Helly Numbers of Polyominoes |
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Authors: | Jean Cardinal Hiro Ito Matias Korman Stefan Langerman |
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Affiliation: | 1. Computer Science Department, Université Libre de Bruxelles (ULB), Brussels, Belgium 2. School of Informatics, Kyoto University, Kyoto, Japan
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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 ≠ 1, 3. |
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