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We show that for any colouring of the edges of the complete bipartite graph$K_{n,n}$ with 3 colours there are 5 disjoint monochromatic cycles whichtogether cover all but $o(n)$ of the vertices. In the same situation, 18disjoint monochromatic cycles together cover all vertices.

Almost partitioning a 3-edge-coloured $K_{n,n}$ into 5 monochromatic cycles