Chromatic uniqueness of elements of height ≤ 3 in lattices of complete multipartite graphs

Abstract

For integers n and t such that 0 <t <n and a nonnegative integer h ≤ 3, it is proved that any complete t-partite n-graph with nontrivial parts and height h in the lattice NPL(n, t) of partitions of the positive integer n into t additive terms is chromatically unique. © 2012 Pleiades Publishing, Ltd.