Koska, Anna On partition graphs. (English) Zbl 0545.05056 Discuss. Math. 6, 59-64 (1983). The vertex set of a partition graph \(G^ n_ 1=\Pi^ n,E_ 1)\) is formed by all partitions of an n-element set A in nonvoid subsets except the trivial partition formed by A itself. Two vertices of \(G^ n_ 1\) are joined by an edge iff the corresponding partitions have at least one common class. The author proves that for each n the partition graph \(G^ n_ 1\) is connected and for \(n>3\) its diameter is equal 3. Density of partition graphs is also studied. Reviewer: H.Kramer MSC: 05C99 Graph theory 05C40 Connectivity Keywords:partition graph of a set; diameter PDFBibTeX XMLCite \textit{A. Koska}, Discuss. Math. 6, 59--64 (1983; Zbl 0545.05056)