Helly Numbers of Polyominoes

Jean Cardinal; Hiro Ito; Matias Korman; Stefan Langerman

doi:10.1007/s00373-012-1203-x

Helly Numbers of Polyominoes

Jean Cardinal, Hiro Ito, Matias Korman, Stefan Langerman

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

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
Pages (from-to)	1221-1234
Number of pages	14
Journal	Graphs and Combinatorics
Volume	29
Issue number	5
DOIs	https://doi.org/10.1007/s00373-012-1203-x
Publication status	Published - 2013 Sep
Externally published	Yes

ASJC Scopus subject areas

Theoretical Computer Science
Discrete Mathematics and Combinatorics

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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.",

author = "Jean Cardinal and Hiro Ito and Matias Korman and Stefan Langerman",

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AU - Korman, Matias

AU - Langerman, Stefan

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AB - 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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Helly Numbers of Polyominoes

Abstract

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