Improved Bounds for r -Identifying Codes of the Hex Grid
Brendon Stanton · SIAM Journal on Discrete Mathematics · 2011
For any positive integer r, an r-identifying code on a graph G is a set $C\subset V(G)$ such that for every vertex in $V(G)$, the intersection of the radius-r closed neighborhood with C is nonempty and pairwise distinct. For a finite graph, the density of a code is $|C|/|V(G)|$, which naturally extends to a definition of density in certain infinite graphs which are locally finite. We find a code of density less than $5/(6r)$, which is sparser than the prior best construction which has density approximately $8/(9r)$.