ABSTRACT: 

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 is said to be weakly
k-colourable if its vertices can be partitioned into k colour classes such
that no cycle has all of its vertices the same colour.  A cycle system's
chromatic number is the smallest value of k for which the system is weakly
k-colourable.  While colourings of 3-cycle systems, or Steiner triple
systems, have been widely studied, less is known regarding colourings of
m-cycle systems in general.  In this talk, we present some results on weak
colourings of m-cycle systems for which the cycle length m is even, in
particular, the result that for any integers r>=2 and k>=2, there is a
k-chromatic (2r)-cycle system.  We illustrate with examples of
constructions of even cycle systems with prescribed chromatic number.

This talk is based on my masters thesis research at Memorial University of
Newfoundland, supervised by Dr. David Pike.