Odd-cycle decomposition threshold conjecture

For an odd integer $\ell\geqslant 3$, let $\delta_{C_\ell}$ be the asymptotic decomposition threshold of the cycle $C_\ell$: the infimum of those $d$ such that every sufficiently large $C_\ell$-divisible graph of minimum degree at least $dn$ has a $C_\ell$-decomposition.

Odd-cycle decomposition threshold conjecture.

$$\delta_{C_\ell}=\frac{1}{2}+\frac{1}{2(\ell-1)}$$

for all odd $\ell\geqslant 3$.

The displayed value arises from an extremal construction, and the source proves the conjecture for every odd $\ell\geqslant 73$; the remaining smaller odd lengths are not all resolved there.