Show that for any integer $n \geq 0$, the complete graph with $2n + 1$ vertices can be $2$−factorable into $n$ Hamiltonian cycles
A graph $G$ is 2-factorable if and only if it is 2r-regular for some r.
If $G$ is Hamiltonian, then that $G$ has a $2$-factor.
I'm trying by induction but I have problems with the inductive step.