A 2t-cycle system of even order v is a set C of cycles of length 2t whose edges partition the edge-set of Kv−I (i.e., the complete graph minus the 1-factor I). If , a set of cd5852e690bd6f3590de340" title="Click to view the MathML source">v/2t vertex-disjoint cycles of C is a parallel class. If C has no parallel classes, we call such a system unparalleled.
We show that there exists an unparalleled 2t-cycle system of order if and only if v>2t>2.