Erdős–Gyárfás–Pyber monochromatic cycle partition conjecture

Let $r$ be a positive integer, and let an $r$-edge-coloured complete graph be a complete graph whose edges receive one of $r$ colours. Erdős–Gyárfás–Pyber conjecture. The vertices of every $r$-edge-coloured complete graph can be covered with $r$ vertex-disjoint monochromatic cycles. This is the central exact cycle-partition conjecture motivating the paper's approximate results; the supplied text gives no resolution status.