Colouring 4-cycle systems with equitably coloured blocks
An \(m\)-colouring of a 4-cycle system of order \(n\) (i.e., of a decomposition of the complete graph \(K_n\) into 4-cycles) is a colouring of the vertices with \(m\) colours; it is equitable if for every 4-cycle two of the four vertices are coloured with one colour, and the other two with another one of the \(m\) colours. The authors investigate the set \(F(n)\) of integers \(m\) such that there exists an equitably \(m\)-coloured 4-cycle system of order \(n\). They show that \(\min F(n)=3\) for every \(n\equiv 1\pmod 8\), \(n\geq 17\) \([F(9)=\varnothing]\), and prove various further results concerning the set \(F(n)\).
scientific article; zbMATH DE number 2093775