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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
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