Erdős–Gould–Yuster–P conjecture on monochromatic cycle partitions

The cycle partition number of an $r$-colored complete graph is the minimum number of vertex-disjoint monochromatic cycles needed to cover all its vertices.

Erdős–Gould–Yuster–P conjecture. The cycle partition number of any $r$-colored complete graph is at most $r$.

The conjecture proposes a linear sharp-looking bound depending only on the number of colors, improving the previously stated quadratic-logarithmic upper bound. The source gives no resolution.