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

Abstract

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 and 18 disjoint monochromatic cycles which together cover all vertices.