TY - JOUR
T1 - Helly Numbers of Polyominoes
AU - Cardinal, Jean
AU - Ito, Hiro
AU - Korman, Matias
AU - Langerman, Stefan
PY - 2013/9
Y1 - 2013/9
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 polyominoes 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 polyominoes of Helly number k for any k ≠ 1, 3.
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U2 - 10.1007/s00373-012-1203-x
DO - 10.1007/s00373-012-1203-x
M3 - Article
AN - SCOPUS:84882824503
SN - 0911-0119
VL - 29
SP - 1221
EP - 1234
JO - Graphs and Combinatorics
JF - Graphs and Combinatorics
IS - 5
ER -