Colouring even cycle systems

Citations of this article
Mendeley users who have this article in their library.


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.

Register to see more suggestions

Mendeley helps you to discover research relevant for your work.

Already have an account?

Save time finding and organizing research with Mendeley

Sign up for free