Disjoint blocking sets in cycle systems Original Research Article

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 Ci of length m such that each edge of the complete graph Kn belongs to precisely one cycle Ci∈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⩽2m/(em)) 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).