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The chromaticity of some families of complete tripartite graphs. (English) Zbl 0760.05037
Via the notion of chromatic polynomial of a graph the authors demonstrate that the following families of complete tripartite graphs are chromatically unique:
$$K(n,n,n+k)$$ for $$n\geq 2$$, $$0\leq k\leq 3$$;
$$K(n-k,n,n+k)$$ for $$n\geq 5$$, $$0\leq k\leq 2$$;
$$K(n-k,n,n)$$ if $$0\leq k\leq 3$$ and $$n\geq k+2$$.
Some open problems and conjectures are posed too.
Reviewer: J.Fiamcik

##### MSC:
 05C15 Coloring of graphs and hypergraphs