Some equitably 3-colourable cycle decompositions
An \(m\)-cycle is equitably \(k\)-coloured if the vertices of the cycle are coloured so that for each two colours the number of vertices of one colour and the number of the other differ by at most one. An \(m\)-cycle decomposition of a graph \(G\) is equitably \(k\)-coloured if the vertices of \(G\) are assigned colours so that each \(m\)-cycle in the decomposition is equitably \(k\)-coloured. For \(m\in \{4,5,6\}\), conditions for the existence of an equitably \(k\)-coloured \(m\)-cycle decomposition of the complete graph, and of the complete graph minus a perfect matching, are determined.
scientific article; zbMATH DE number 2093764