Helly Numbers of Polyominoes

08/21/2017

∙

by   Jean Cardinal, et al.

∙

0

∙

share

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.