I am interested in coverings of complete graph $K_n$ by cycles of length $4$. It is clear that covering always exist when $n \ge 3$. I need to find minimal number of $4$-cycles to cover $K_n$.

For example $K_5$ can be covered by following cycles $(1, 2, 3, 5), (2, 5, 4, 3), (2, 4, 1, 3)$.

I am sure this problem has studied but unfortunately cant find any results. Can you share some results?