Helly Numbers of Polyominoes

Jean Cardinal, Hiro Ito, Matias Korman, Stefan Langerman

Research output: Contribution to journalArticlepeer-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 languageEnglish
Pages (from-to)1221-1234
Number of pages14
JournalGraphs and Combinatorics
Volume29
Issue number5
DOIs
Publication statusPublished - 2013 Sep
Externally publishedYes

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics

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