Almost partitioning a 3-edge-coloured Kn,n into 5 monochromatic cycles
Abstract
We show that for any colouring of the edges of the complete bipartite graph Kn,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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