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

preprint2016arXivOpen access

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 which together cover all but $o(n)$ of the vertices. In the same situation, 18 disjoint monochromatic cycles together cover all vertices.

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

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Almost partitioning a 3-edge-coloured Kn,nK_{n,n}Kn,n​ into 5 monochromatic cycles

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