Chromatic uniqueness of atoms in lattices of complete multipartite graphs

A new approach is suggested to the study of the chromatic uniqueness of complete multipartite graphs. The approach is based on the natural lattice order introduced for such graphs. It is proved that atoms with nonelemental partite sets are chromatically unique in the lattice of complete $t$-partite $n$-graphs for any given positive integers $n$ and $t$.