4-Cycle Systems of $$K_n - E(F^*)$$ K n - E ( F ∗ )

In this paper necessary and sufficient conditions are found for the existence of a $$4$$4-cycle system of a complete graph on $$n$$n vertices with leave a nearly $$2$$2-regular graph (that is, a not necessarily spanning graph in which all vertices have degree 2 except for one of degree greater than 2).