An i-packing in a graph G is a set of vertices at pairwise distance
greater than i. For a nondecreasing sequence of integers
S=(s_1,s_2,…), the S-packing chromatic number of a graph G is
the least integer k such that there exists a coloring of G into k colors
where each set of vertices colored i, i=1,…,k, is an s_i-packing.
This paper describes various subdivisions of an i-packing into j-packings
(j\textgreater{}i) for the hexagonal, square and triangular lattices. These
results allow us to bound the S-packing chromatic number for these graphs,
with more precise bounds and exact values for sequences S=(s_i,i∈N∗), s_i=d+⌊(i−1)/n⌋