Helly numbers of polyominoes

Jean Cardinal; Hiro Ito; Matias Korman; Stefan Langerman

Helly numbers of polyominoes

Jean Cardinal, Hiro Ito, Matias Korman, Stefan Langerman

Research output: Contribution to conference › Paper › peer-review

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 polyminoes of Helly number k for any k ≠ 1, 3.

Original language	English
Publication status	Published - 2011 Dec 1
Externally published	Yes
Event	23rd Annual Canadian Conference on Computational Geometry, CCCG 2011 - Toronto, ON, Canada Duration: 2011 Aug 10 → 2011 Aug 12

Other

Other	23rd Annual Canadian Conference on Computational Geometry, CCCG 2011
Country/Territory	Canada
City	Toronto, ON
Period	11/8/10 → 11/8/12

ASJC Scopus subject areas

Computational Mathematics
Geometry and Topology

Cite this

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title = "Helly numbers of polyominoes",

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 polyminoes 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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language = "English",

note = "23rd Annual Canadian Conference on Computational Geometry, CCCG 2011 ; Conference date: 10-08-2011 Through 12-08-2011",

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T1 - Helly numbers of polyominoes

AU - Cardinal, Jean

AU - Ito, Hiro

AU - Korman, Matias

AU - Langerman, Stefan

PY - 2011/12/1

Y1 - 2011/12/1

N2 - 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 polyminoes of Helly number k for any k ≠ 1, 3.

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 polyminoes of Helly number k for any k ≠ 1, 3.

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UR - http://www.scopus.com/inward/citedby.url?scp=84882968705&partnerID=8YFLogxK

M3 - Paper

AN - SCOPUS:84882968705

T2 - 23rd Annual Canadian Conference on Computational Geometry, CCCG 2011

Y2 - 10 August 2011 through 12 August 2011

ER -

Helly numbers of polyominoes

Abstract

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ASJC Scopus subject areas

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