Classification of elements of small height in lattices of complete multipartite graphs

The purpose of the paper is to classify elements of height 2 and 3 in lattices $NPL(n,t)$ of complete multipartite graphs for $t\ge4$. In addition, lower floors of the lattices $NPL(n,t)$ are described and information on two chromatic invariants is specified. This information is used for studying the chromatic uniqueness of complete multipartite graphs.