Disjoint blocking sets in cycle systems

Abstract In an m -cycle system C of order n (n⩾m⩾3 integers) , the blocks are the vertex sets of n(n−1)/(2m) cycles C i of length m such that each edge of the complete graph K n belongs to precisely one cycle C i ∈ C . We investigate m -cycle systems which admit vertex partitions into two or more classes in such a way that each class meets every cycle of C . Relatively small systems (with n⩽2 m /( e m) ) are always ‘2-colorable’ in this sense; moreover, for every constant c, if n⩽cm , then a partition into c′m/ log m classes exists (where the constant c′ depends only on c ).