An m-cycle system of order n is a partition of the edges of the complete graph K n into m-cycles. An m-cycle system S is said to be weakly k-colourable if its vertices may be partitioned into k sets (called colour classes) such that no m-cycle in S has all of its vertices the same colour. The smallest value of k for which a cycle system S admits a weak k-colouring is called the chromatic number of S. We study weak colourings of even cycle systems (i.e. m-cycle systems for which m is even), and show that for any integers r ≥ 2 and k ≥ 2, there is a (2 r)-cycle system with chromatic number k. © 2007 Elsevier B.V. All rights reserved.
Burgess, A. C., & Pike, D. A. (2008). Colouring even cycle systems. Discrete Mathematics, 308(5–6), 962–973. https://doi.org/10.1016/j.disc.2007.07.115