Amount of 3-cycle in complete graph.

Question

Consider the complete graph $ K_n $ .

How much is disjoint cycles of length three? Thanks in advance.

Answer 1

I shall interpret disjoint as edge-disjoint. This question was already considered at MatOverfolw. I can remark that the graph $K_n$ has ${n \choose 2}$ edges, so it can have at most ${n \choose 2}/3$ disjoint 3-cycles. I expect that this upper bound differs from the exact value by $o(1)$.