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.
Original language | English |
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Pages (from-to) | 1221-1234 |
Number of pages | 14 |
Journal | Graphs and Combinatorics |
Volume | 29 |
Issue number | 5 |
DOIs | |
Publication status | Published - 2013 Sep |
Externally published | Yes |
ASJC Scopus subject areas
- Theoretical Computer Science
- Discrete Mathematics and Combinatorics