  We say that a vertex-coloring of a graph is a proper k-distance domatic
coloring if for each color, every vertex is within distance k from a vertex
receiving that color. The maximum number of colors for which such a coloring
exists is called the k-distance domatic number of the graph. The problem of
determining the k-distance domatic number is motivated by questions about
multi-agent networks including arrangements of sensors and robotics. Here, we
find the exact k-distance domatic numbers for all grid graphs formed from the
Cartesian product of two sufficiently long paths.
