Abstract
An r-identifying code in a graph G=(V,E) is a subset C⊆V such that for each u∈V the intersection of C and the ball of radius r centered at u is nonempty and unique. Previously, r-identifying codes have been studied in various grids. In particular, it has been shown that there exists a 2-identifying code in the square grid with density 5/29≈0.172 and that there are no 2-identifying codes with density smaller than 3/20=0.15. Recently, the lower bound has been improved to 6/37≈0.162 by Martin and Stanton (2010) [11]. In this paper, we further improve the lower bound by showing that there are no 2-identifying codes in the square grid with density smaller than 6/35≈0.171.
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