Erdős–Simonovits–Sós rainbow cycle conjecture

Let $G$ be an edge-colored graph of order $n$, and let $c(G)$ denote the number of colors appearing on its edges. Erdős–Simonovits–Sós conjecture. For all $n\geq k\geq 3$, if

$$c(G) \geq \left(\frac{k-2}{2}+\frac{1}{k-1}\right)n+O(1),$$

then $G$ contains a rainbow cycle $C_k$. This conjecture gives a color-degree threshold forcing rainbow cycles and is part of the anti-Ramsey theory of edge-colored graphs; the supplied source does not indicate whether it has been resolved.