Keevash–Mubayi–Sudakov–Verstraëte rainbow-cycle conjecture

Let $G$ be a properly edge-colored graph on $n$ vertices, meaning that no two edges incident with the same vertex have the same color. A rainbow cycle is a cycle whose edges all have distinct colors.

Keevash–Mubayi–Sudakov–Verstraëte conjecture. There is a constant $C$ such that every properly edge-colored $n$-vertex graph with at least $Cn\log n$ edges contains a rainbow cycle.

The statement is motivated by a construction with $\Omega(n\log n)$ edges and is presented as the conjectured sharp order of magnitude. Its resolution is not given in the supplied text.