On the existence of unparalleled even cycle systems. (January 2017) - Danziger, Peter; Mendelsohn, Eric; Traetta, Tommaso
Abstract: A 2 t -cycle system of even order v is a set C of cycles of length 2 t whose edges partition the edge-set of K v − I (i.e., the complete graph minus the 1 -factor I ). If v ≡ 0 ( mod 2 t ), a set of v / 2 t 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 2 t -cycle system of order v ≡ 0 ( mod 2 t ) if and only if v > 2 t > 2 .