Voloshin's colourings of \(P_{3}\)-designs
The mixed hypergraph coloring problem is to color the vertex set of a hypergraph in such a way that some hyperedges (called \(\mathcal C\)-edges) contain at least two vertices in a common color and some (called \(\mathcal D\)-edges) contain vertices in at least two different colors. This general problem was introduced by \textit{V. I. Voloshin} [Coloring mixed hypergraphs: theory, algorithms and applications (Fields Institute Monographs. 17. Providence) (2002; Zbl 1001.05003)]. The present author considers the special case of \(P_3\) designs, where he regards each block both as a \(\mathcal C\)-edge and a \(\mathcal D\)-edge. In other words, he is looking for colorings of such designs such that each block contains exactly two different colors. He constructs several \(P_3\)-designs having particular properties of mixed hypergraphs like broken spectrum, equal lower and upper chromatic number and others.
scientific article; zbMATH DE number 2035869